Lectures on Finsler geometry /:
In 1854, B. Riemann introduced the notion of curvature for spaces with a family of inner products. There was no significant progress in the general case until 1918, when P. Finsler studied the variation problem in regular metric spaces. Around 1926, L. Berwald extended Riemann's notion of curva...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Singapore ; River Edge, NJ :
World Scientific,
©2001.
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| Online-Zugang: | Volltext |
| Zusammenfassung: | In 1854, B. Riemann introduced the notion of curvature for spaces with a family of inner products. There was no significant progress in the general case until 1918, when P. Finsler studied the variation problem in regular metric spaces. Around 1926, L. Berwald extended Riemann's notion of curvature to regular metric spaces and introduced an important non-Riemannian curvature using his connection for regular metrics. Since then, Finsler geometry has developed steadily. In his Paris address in 1900, D. Hilbert formulated 23 problems, the 4th and 23rd problems being in Finsler's category. Finsler geometry has broader applications in many areas of science and will continue to develop through the efforts of many geometers around the world. Usually, the methods employed in Finsler geometry involve very complicated tensor computations. Sometimes this discourages beginners. Viewing Finsler spaces as regular metric spaces, the author discusses the problems from the modern geometry point of view. The book begins with the basics on Finsler spaces, including the notions of geodesics and curvatures, then deals with basic comparison theorems on metrics and measures and their applications to the Levy concentration theory of regular metric measure spaces and Gromov's Hausdorff convergence theory. |
| Beschreibung: | 1 online resource (xiv, 307 pages :) |
| Bibliographie: | Includes bibliographical references (pages 299-304) and index. |
| ISBN: | 9789812811622 9812811621 1281960659 9781281960658 9789810245313 9810245319 |
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| 245 | 1 | 0 | |a Lectures on Finsler geometry / |c Zhongmin Shen. |
| 260 | |a Singapore ; |a River Edge, NJ : |b World Scientific, |c ©2001. | ||
| 300 | |a 1 online resource (xiv, 307 pages :) | ||
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| 504 | |a Includes bibliographical references (pages 299-304) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a In 1854, B. Riemann introduced the notion of curvature for spaces with a family of inner products. There was no significant progress in the general case until 1918, when P. Finsler studied the variation problem in regular metric spaces. Around 1926, L. Berwald extended Riemann's notion of curvature to regular metric spaces and introduced an important non-Riemannian curvature using his connection for regular metrics. Since then, Finsler geometry has developed steadily. In his Paris address in 1900, D. Hilbert formulated 23 problems, the 4th and 23rd problems being in Finsler's category. Finsler geometry has broader applications in many areas of science and will continue to develop through the efforts of many geometers around the world. Usually, the methods employed in Finsler geometry involve very complicated tensor computations. Sometimes this discourages beginners. Viewing Finsler spaces as regular metric spaces, the author discusses the problems from the modern geometry point of view. The book begins with the basics on Finsler spaces, including the notions of geodesics and curvatures, then deals with basic comparison theorems on metrics and measures and their applications to the Levy concentration theory of regular metric measure spaces and Gromov's Hausdorff convergence theory. | ||
| 505 | 0 | |a Ch. 1. Finsler spaces. 1.1. Metric spaces. 1.2. Minkowski spaces. 1.3. Finsler spaces -- ch. 2. Finsler m spaces. 2.1. Measure spaces. 2.2. Volume on a Finsler space. 2.3. Hyperplanes in a Minkowski m space. 2.4. Hypersurfaces in a Finsler m space -- ch. 3. Co-area formula. 3.1. Legendre transformations. 3.2. Gradients of functions. 3.3. Co-area formula -- ch. 4. Isoperimetric inequalities. 4.1. Isoperirnetric profiles. 4.2. Sobolev constants and first eigenvalue. 4.3. Concentration of Finsler m spaces. 4.4. Observable diameter -- ch. 5. Geodesies and connection. 5.1. Geodesies. 5.2. Chern connection. 5.3. Covariant derivatives. 5.4. Geodesic flow -- ch. 6. Riemann curvature. 6.1. Birth of the Riemann curvature. 6.2. Geodesic fields. 6.3. Projectively related Finsler metrics -- ch. 7. Non-Riemannian curvatures. 7.1. Cartan torsion. 7.2. Chern curvature. 7.3. S-curvature -- ch. 8. Structure equations. 8.1. Structure equations of Finsler spaces. 8.2. Structure equations of Riemannian metrics. 8.3. Riemann curvature of randers metrics -- ch. 9. Finsler spaces of constant curvature. 9.1. Finsler metrics of constant curvature. 9.2. Examples. 9.3. Randers metrics of constant curvature -- ch. 10. Second variation formula. 10.1. T-curvature. 10.2. Second variation of length. 10.3. Synge theorem -- ch. 11. Geodesies and exponential map. 11.1. Exponential map. 11.2. Jacobi fields. 11.3. Minimality of geodesies. 11.4. Completeness of Finsler spaces -- ch. 12. Conjugate radius and injectivity radius. 12.1. Conjugate radius. 12.2. Injectivity radius. 12.3. Geodesic loops and closed geodesies -- ch. 13. Basic comparison theorems. 13.1. Flag curvature bounded above. 13.2. Positive flag curvature. 13.3. Ricci curvature bounded below. 13.4. Green-Dazord theorem -- ch. 14. Geometry of hypersurfaces. 14.1. Hessian and Laplacian. 14.2. Normal curvature. 14.3. Mean curvature. 14.4. Shape operator -- ch. 15. Geometry of metric spheres. 15.1. Estimates on the normal curvature. 15.2. Convexity of metric balls. 15.3. Estimates on the mean curvature. 15.4. Metric spheres in a convex domain -- ch. 16. Volume comparison theorems. 16.1. Volume of metric balls. 16.2. Volume of tubular neighborhoods. 16.3. Gromov simplicial norms. 16.4. Estimates on the expansion distance -- ch. 17. Morse theory of loop spaces. 17.1. A review on the morse theory. 17.2. Indexes of geodesic loops. 17.3. Energy functional on a loop space. 17.4. Approximation of loop spaces -- ch. 18. Vanishing theorems for homotopy groups. 18.1. Intermediate curvatures. 18.2. Vanishing theorem for homotopy groups. 18.3. Finsler spaces of positive constant curvature -- ch. 19. Spaces of Finsler spaces. 19.1. Gromov-Hausdorff distance. 19.2. Precompactness theorem. | |
| 650 | 0 | |a Finsler spaces. |0 http://id.loc.gov/authorities/subjects/sh85048439 | |
| 650 | 0 | |a Geometry, Differential. |0 http://id.loc.gov/authorities/subjects/sh85054146 | |
| 650 | 6 | |a Espaces de Finsler. | |
| 650 | 6 | |a Géométrie différentielle. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Analytic. |2 bisacsh | |
| 650 | 7 | |a Finsler spaces |2 fast | |
| 650 | 7 | |a Geometry, Differential |2 fast | |
| 650 | 7 | |a Géométrie différentielle. |2 rvm | |
| 758 | |i has work: |a Lectures on Finsler Geometry (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGcvXcMGv9VbrBPdVchQG3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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| author | Shen, Zhongmin, 1963- |
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| contents | Ch. 1. Finsler spaces. 1.1. Metric spaces. 1.2. Minkowski spaces. 1.3. Finsler spaces -- ch. 2. Finsler m spaces. 2.1. Measure spaces. 2.2. Volume on a Finsler space. 2.3. Hyperplanes in a Minkowski m space. 2.4. Hypersurfaces in a Finsler m space -- ch. 3. Co-area formula. 3.1. Legendre transformations. 3.2. Gradients of functions. 3.3. Co-area formula -- ch. 4. Isoperimetric inequalities. 4.1. Isoperirnetric profiles. 4.2. Sobolev constants and first eigenvalue. 4.3. Concentration of Finsler m spaces. 4.4. Observable diameter -- ch. 5. Geodesies and connection. 5.1. Geodesies. 5.2. Chern connection. 5.3. Covariant derivatives. 5.4. Geodesic flow -- ch. 6. Riemann curvature. 6.1. Birth of the Riemann curvature. 6.2. Geodesic fields. 6.3. Projectively related Finsler metrics -- ch. 7. Non-Riemannian curvatures. 7.1. Cartan torsion. 7.2. Chern curvature. 7.3. S-curvature -- ch. 8. Structure equations. 8.1. Structure equations of Finsler spaces. 8.2. Structure equations of Riemannian metrics. 8.3. Riemann curvature of randers metrics -- ch. 9. Finsler spaces of constant curvature. 9.1. Finsler metrics of constant curvature. 9.2. Examples. 9.3. Randers metrics of constant curvature -- ch. 10. Second variation formula. 10.1. T-curvature. 10.2. Second variation of length. 10.3. Synge theorem -- ch. 11. Geodesies and exponential map. 11.1. Exponential map. 11.2. Jacobi fields. 11.3. Minimality of geodesies. 11.4. Completeness of Finsler spaces -- ch. 12. Conjugate radius and injectivity radius. 12.1. Conjugate radius. 12.2. Injectivity radius. 12.3. Geodesic loops and closed geodesies -- ch. 13. Basic comparison theorems. 13.1. Flag curvature bounded above. 13.2. Positive flag curvature. 13.3. Ricci curvature bounded below. 13.4. Green-Dazord theorem -- ch. 14. Geometry of hypersurfaces. 14.1. Hessian and Laplacian. 14.2. Normal curvature. 14.3. Mean curvature. 14.4. Shape operator -- ch. 15. Geometry of metric spheres. 15.1. Estimates on the normal curvature. 15.2. Convexity of metric balls. 15.3. Estimates on the mean curvature. 15.4. Metric spheres in a convex domain -- ch. 16. Volume comparison theorems. 16.1. Volume of metric balls. 16.2. Volume of tubular neighborhoods. 16.3. Gromov simplicial norms. 16.4. Estimates on the expansion distance -- ch. 17. Morse theory of loop spaces. 17.1. A review on the morse theory. 17.2. Indexes of geodesic loops. 17.3. Energy functional on a loop space. 17.4. Approximation of loop spaces -- ch. 18. Vanishing theorems for homotopy groups. 18.1. Intermediate curvatures. 18.2. Vanishing theorem for homotopy groups. 18.3. Finsler spaces of positive constant curvature -- ch. 19. Spaces of Finsler spaces. 19.1. Gromov-Hausdorff distance. 19.2. Precompactness theorem. |
| ctrlnum | (OCoLC)261336333 |
| dewey-full | 516.3/73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/73 |
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| discipline | Mathematik |
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Shen.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Singapore ;</subfield><subfield code="a">River Edge, NJ :</subfield><subfield code="b">World Scientific,</subfield><subfield code="c">©2001.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xiv, 307 pages :)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 299-304) and index.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In 1854, B. Riemann introduced the notion of curvature for spaces with a family of inner products. There was no significant progress in the general case until 1918, when P. Finsler studied the variation problem in regular metric spaces. Around 1926, L. Berwald extended Riemann's notion of curvature to regular metric spaces and introduced an important non-Riemannian curvature using his connection for regular metrics. Since then, Finsler geometry has developed steadily. In his Paris address in 1900, D. Hilbert formulated 23 problems, the 4th and 23rd problems being in Finsler's category. Finsler geometry has broader applications in many areas of science and will continue to develop through the efforts of many geometers around the world. Usually, the methods employed in Finsler geometry involve very complicated tensor computations. Sometimes this discourages beginners. Viewing Finsler spaces as regular metric spaces, the author discusses the problems from the modern geometry point of view. The book begins with the basics on Finsler spaces, including the notions of geodesics and curvatures, then deals with basic comparison theorems on metrics and measures and their applications to the Levy concentration theory of regular metric measure spaces and Gromov's Hausdorff convergence theory.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Ch. 1. Finsler spaces. 1.1. Metric spaces. 1.2. Minkowski spaces. 1.3. Finsler spaces -- ch. 2. Finsler m spaces. 2.1. Measure spaces. 2.2. Volume on a Finsler space. 2.3. Hyperplanes in a Minkowski m space. 2.4. Hypersurfaces in a Finsler m space -- ch. 3. Co-area formula. 3.1. Legendre transformations. 3.2. Gradients of functions. 3.3. Co-area formula -- ch. 4. Isoperimetric inequalities. 4.1. Isoperirnetric profiles. 4.2. Sobolev constants and first eigenvalue. 4.3. Concentration of Finsler m spaces. 4.4. Observable diameter -- ch. 5. Geodesies and connection. 5.1. Geodesies. 5.2. Chern connection. 5.3. Covariant derivatives. 5.4. Geodesic flow -- ch. 6. Riemann curvature. 6.1. Birth of the Riemann curvature. 6.2. Geodesic fields. 6.3. Projectively related Finsler metrics -- ch. 7. Non-Riemannian curvatures. 7.1. Cartan torsion. 7.2. Chern curvature. 7.3. S-curvature -- ch. 8. Structure equations. 8.1. Structure equations of Finsler spaces. 8.2. Structure equations of Riemannian metrics. 8.3. Riemann curvature of randers metrics -- ch. 9. Finsler spaces of constant curvature. 9.1. Finsler metrics of constant curvature. 9.2. Examples. 9.3. Randers metrics of constant curvature -- ch. 10. Second variation formula. 10.1. T-curvature. 10.2. Second variation of length. 10.3. Synge theorem -- ch. 11. Geodesies and exponential map. 11.1. Exponential map. 11.2. Jacobi fields. 11.3. Minimality of geodesies. 11.4. Completeness of Finsler spaces -- ch. 12. Conjugate radius and injectivity radius. 12.1. Conjugate radius. 12.2. Injectivity radius. 12.3. Geodesic loops and closed geodesies -- ch. 13. Basic comparison theorems. 13.1. Flag curvature bounded above. 13.2. Positive flag curvature. 13.3. Ricci curvature bounded below. 13.4. Green-Dazord theorem -- ch. 14. Geometry of hypersurfaces. 14.1. Hessian and Laplacian. 14.2. Normal curvature. 14.3. Mean curvature. 14.4. Shape operator -- ch. 15. Geometry of metric spheres. 15.1. Estimates on the normal curvature. 15.2. Convexity of metric balls. 15.3. Estimates on the mean curvature. 15.4. Metric spheres in a convex domain -- ch. 16. Volume comparison theorems. 16.1. Volume of metric balls. 16.2. Volume of tubular neighborhoods. 16.3. Gromov simplicial norms. 16.4. Estimates on the expansion distance -- ch. 17. Morse theory of loop spaces. 17.1. A review on the morse theory. 17.2. Indexes of geodesic loops. 17.3. Energy functional on a loop space. 17.4. Approximation of loop spaces -- ch. 18. Vanishing theorems for homotopy groups. 18.1. Intermediate curvatures. 18.2. Vanishing theorem for homotopy groups. 18.3. Finsler spaces of positive constant curvature -- ch. 19. Spaces of Finsler spaces. 19.1. Gromov-Hausdorff distance. 19.2. Precompactness theorem.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Finsler spaces.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85048439</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Geometry, Differential.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85054146</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Espaces de Finsler.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Géométrie différentielle.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Geometry</subfield><subfield code="x">Analytic.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Finsler spaces</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Geometry, Differential</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Géométrie différentielle.</subfield><subfield code="2">rvm</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Lectures on Finsler Geometry (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCGcvXcMGv9VbrBPdVchQG3</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Shen, Zhongmin, 1963-</subfield><subfield code="t">Lectures on Finsler geometry.</subfield><subfield code="d">Singapore ; River Edge, NJ : World Scientific, ©2001</subfield><subfield code="z">9810245300</subfield><subfield code="z">9789810245306</subfield><subfield code="w">(DLC) 2005297899</subfield><subfield code="w">(OCoLC)47797302</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235868</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">CBO01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235868</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH24685634</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest Ebook Central</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL1681622</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10256005</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">235868</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">196065</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">2889345</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn261336333 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:16:55Z |
| institution | BVB |
| isbn | 9789812811622 9812811621 1281960659 9781281960658 9789810245313 9810245319 |
| language | English |
| oclc_num | 261336333 |
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| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (xiv, 307 pages :) |
| psigel | ZDB-4-EBA |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Shen, Zhongmin, 1963- https://id.oclc.org/worldcat/entity/E39PCjrTbtCdD7qvmwqvc3X8G3 http://id.loc.gov/authorities/names/n96044362 Lectures on Finsler geometry / Zhongmin Shen. Singapore ; River Edge, NJ : World Scientific, ©2001. 1 online resource (xiv, 307 pages :) text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 299-304) and index. Print version record. In 1854, B. Riemann introduced the notion of curvature for spaces with a family of inner products. There was no significant progress in the general case until 1918, when P. Finsler studied the variation problem in regular metric spaces. Around 1926, L. Berwald extended Riemann's notion of curvature to regular metric spaces and introduced an important non-Riemannian curvature using his connection for regular metrics. Since then, Finsler geometry has developed steadily. In his Paris address in 1900, D. Hilbert formulated 23 problems, the 4th and 23rd problems being in Finsler's category. Finsler geometry has broader applications in many areas of science and will continue to develop through the efforts of many geometers around the world. Usually, the methods employed in Finsler geometry involve very complicated tensor computations. Sometimes this discourages beginners. Viewing Finsler spaces as regular metric spaces, the author discusses the problems from the modern geometry point of view. The book begins with the basics on Finsler spaces, including the notions of geodesics and curvatures, then deals with basic comparison theorems on metrics and measures and their applications to the Levy concentration theory of regular metric measure spaces and Gromov's Hausdorff convergence theory. Ch. 1. Finsler spaces. 1.1. Metric spaces. 1.2. Minkowski spaces. 1.3. Finsler spaces -- ch. 2. Finsler m spaces. 2.1. Measure spaces. 2.2. Volume on a Finsler space. 2.3. Hyperplanes in a Minkowski m space. 2.4. Hypersurfaces in a Finsler m space -- ch. 3. Co-area formula. 3.1. Legendre transformations. 3.2. Gradients of functions. 3.3. Co-area formula -- ch. 4. Isoperimetric inequalities. 4.1. Isoperirnetric profiles. 4.2. Sobolev constants and first eigenvalue. 4.3. Concentration of Finsler m spaces. 4.4. Observable diameter -- ch. 5. Geodesies and connection. 5.1. Geodesies. 5.2. Chern connection. 5.3. Covariant derivatives. 5.4. Geodesic flow -- ch. 6. Riemann curvature. 6.1. Birth of the Riemann curvature. 6.2. Geodesic fields. 6.3. Projectively related Finsler metrics -- ch. 7. Non-Riemannian curvatures. 7.1. Cartan torsion. 7.2. Chern curvature. 7.3. S-curvature -- ch. 8. Structure equations. 8.1. Structure equations of Finsler spaces. 8.2. Structure equations of Riemannian metrics. 8.3. Riemann curvature of randers metrics -- ch. 9. Finsler spaces of constant curvature. 9.1. Finsler metrics of constant curvature. 9.2. Examples. 9.3. Randers metrics of constant curvature -- ch. 10. Second variation formula. 10.1. T-curvature. 10.2. Second variation of length. 10.3. Synge theorem -- ch. 11. Geodesies and exponential map. 11.1. Exponential map. 11.2. Jacobi fields. 11.3. Minimality of geodesies. 11.4. Completeness of Finsler spaces -- ch. 12. Conjugate radius and injectivity radius. 12.1. Conjugate radius. 12.2. Injectivity radius. 12.3. Geodesic loops and closed geodesies -- ch. 13. Basic comparison theorems. 13.1. Flag curvature bounded above. 13.2. Positive flag curvature. 13.3. Ricci curvature bounded below. 13.4. Green-Dazord theorem -- ch. 14. Geometry of hypersurfaces. 14.1. Hessian and Laplacian. 14.2. Normal curvature. 14.3. Mean curvature. 14.4. Shape operator -- ch. 15. Geometry of metric spheres. 15.1. Estimates on the normal curvature. 15.2. Convexity of metric balls. 15.3. Estimates on the mean curvature. 15.4. Metric spheres in a convex domain -- ch. 16. Volume comparison theorems. 16.1. Volume of metric balls. 16.2. Volume of tubular neighborhoods. 16.3. Gromov simplicial norms. 16.4. Estimates on the expansion distance -- ch. 17. Morse theory of loop spaces. 17.1. A review on the morse theory. 17.2. Indexes of geodesic loops. 17.3. Energy functional on a loop space. 17.4. Approximation of loop spaces -- ch. 18. Vanishing theorems for homotopy groups. 18.1. Intermediate curvatures. 18.2. Vanishing theorem for homotopy groups. 18.3. Finsler spaces of positive constant curvature -- ch. 19. Spaces of Finsler spaces. 19.1. Gromov-Hausdorff distance. 19.2. Precompactness theorem. Finsler spaces. http://id.loc.gov/authorities/subjects/sh85048439 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Espaces de Finsler. Géométrie différentielle. MATHEMATICS Geometry Analytic. bisacsh Finsler spaces fast Geometry, Differential fast Géométrie différentielle. rvm has work: Lectures on Finsler Geometry (Text) https://id.oclc.org/worldcat/entity/E39PCGcvXcMGv9VbrBPdVchQG3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Shen, Zhongmin, 1963- Lectures on Finsler geometry. Singapore ; River Edge, NJ : World Scientific, ©2001 9810245300 9789810245306 (DLC) 2005297899 (OCoLC)47797302 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235868 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235868 Volltext |
| spellingShingle | Shen, Zhongmin, 1963- Lectures on Finsler geometry / Ch. 1. Finsler spaces. 1.1. Metric spaces. 1.2. Minkowski spaces. 1.3. Finsler spaces -- ch. 2. Finsler m spaces. 2.1. Measure spaces. 2.2. Volume on a Finsler space. 2.3. Hyperplanes in a Minkowski m space. 2.4. Hypersurfaces in a Finsler m space -- ch. 3. Co-area formula. 3.1. Legendre transformations. 3.2. Gradients of functions. 3.3. Co-area formula -- ch. 4. Isoperimetric inequalities. 4.1. Isoperirnetric profiles. 4.2. Sobolev constants and first eigenvalue. 4.3. Concentration of Finsler m spaces. 4.4. Observable diameter -- ch. 5. Geodesies and connection. 5.1. Geodesies. 5.2. Chern connection. 5.3. Covariant derivatives. 5.4. Geodesic flow -- ch. 6. Riemann curvature. 6.1. Birth of the Riemann curvature. 6.2. Geodesic fields. 6.3. Projectively related Finsler metrics -- ch. 7. Non-Riemannian curvatures. 7.1. Cartan torsion. 7.2. Chern curvature. 7.3. S-curvature -- ch. 8. Structure equations. 8.1. Structure equations of Finsler spaces. 8.2. Structure equations of Riemannian metrics. 8.3. Riemann curvature of randers metrics -- ch. 9. Finsler spaces of constant curvature. 9.1. Finsler metrics of constant curvature. 9.2. Examples. 9.3. Randers metrics of constant curvature -- ch. 10. Second variation formula. 10.1. T-curvature. 10.2. Second variation of length. 10.3. Synge theorem -- ch. 11. Geodesies and exponential map. 11.1. Exponential map. 11.2. Jacobi fields. 11.3. Minimality of geodesies. 11.4. Completeness of Finsler spaces -- ch. 12. Conjugate radius and injectivity radius. 12.1. Conjugate radius. 12.2. Injectivity radius. 12.3. Geodesic loops and closed geodesies -- ch. 13. Basic comparison theorems. 13.1. Flag curvature bounded above. 13.2. Positive flag curvature. 13.3. Ricci curvature bounded below. 13.4. Green-Dazord theorem -- ch. 14. Geometry of hypersurfaces. 14.1. Hessian and Laplacian. 14.2. Normal curvature. 14.3. Mean curvature. 14.4. Shape operator -- ch. 15. Geometry of metric spheres. 15.1. Estimates on the normal curvature. 15.2. Convexity of metric balls. 15.3. Estimates on the mean curvature. 15.4. Metric spheres in a convex domain -- ch. 16. Volume comparison theorems. 16.1. Volume of metric balls. 16.2. Volume of tubular neighborhoods. 16.3. Gromov simplicial norms. 16.4. Estimates on the expansion distance -- ch. 17. Morse theory of loop spaces. 17.1. A review on the morse theory. 17.2. Indexes of geodesic loops. 17.3. Energy functional on a loop space. 17.4. Approximation of loop spaces -- ch. 18. Vanishing theorems for homotopy groups. 18.1. Intermediate curvatures. 18.2. Vanishing theorem for homotopy groups. 18.3. Finsler spaces of positive constant curvature -- ch. 19. Spaces of Finsler spaces. 19.1. Gromov-Hausdorff distance. 19.2. Precompactness theorem. Finsler spaces. http://id.loc.gov/authorities/subjects/sh85048439 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Espaces de Finsler. Géométrie différentielle. MATHEMATICS Geometry Analytic. bisacsh Finsler spaces fast Geometry, Differential fast Géométrie différentielle. rvm |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85048439 http://id.loc.gov/authorities/subjects/sh85054146 |
| title | Lectures on Finsler geometry / |
| title_auth | Lectures on Finsler geometry / |
| title_exact_search | Lectures on Finsler geometry / |
| title_full | Lectures on Finsler geometry / Zhongmin Shen. |
| title_fullStr | Lectures on Finsler geometry / Zhongmin Shen. |
| title_full_unstemmed | Lectures on Finsler geometry / Zhongmin Shen. |
| title_short | Lectures on Finsler geometry / |
| title_sort | lectures on finsler geometry |
| topic | Finsler spaces. http://id.loc.gov/authorities/subjects/sh85048439 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Espaces de Finsler. Géométrie différentielle. MATHEMATICS Geometry Analytic. bisacsh Finsler spaces fast Geometry, Differential fast Géométrie différentielle. rvm |
| topic_facet | Finsler spaces. Geometry, Differential. Espaces de Finsler. Géométrie différentielle. MATHEMATICS Geometry Analytic. Finsler spaces Geometry, Differential Géométrie différentielle. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235868 |
| work_keys_str_mv | AT shenzhongmin lecturesonfinslergeometry |