Pseudo-Riemannian geometry, [delta]-invariants and applications /:
Pseudo-Riemannian geometry, δ-invariants and applications /
The first part of this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold theory. A number of recent results on pseudo...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore :
World Scientific,
©2011.
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| Online-Zugang: | Volltext |
| Zusammenfassung: | The first part of this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold theory. A number of recent results on pseudo-Riemannian submanifolds are also included. The second part of this book is on [symbol]-invariants, which was introduced in the early 1990s by the author. The famous Nash embedding theorem published in 1956 was aimed for, in the hope that if Riemannian manifolds could be regarded as Riemannian submanifolds, this would then yield the opportunity to use extrinsic help. However, this hope had not been materialized as pointed out by M. Gromov in his 1985 article published in Asterisque. The main reason for this is the lack of control of the extrinsic invariants of the submanifolds by known intrinsic invariants. In order to overcome such difficulties, as well as to provide answers for an open question on minimal immersions, the author introduced in the early 1990s new types of Riemannian invariants, known as [symbol]-invariants, which are very different in nature from the classical Ricci and scalar curvatures. At the same time he was able to establish general optimal relations between [symbol]-invariants and the main extrinsic invariants. Since then many new results concerning these [symbol]-invariants have been obtained by many geometers. The second part of this book is to provide an extensive and comprehensive survey over this very active field of research done during the last two decades. |
| Beschreibung: | 1 online resource (xxxii, 477 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 439-462) and indexes. |
| ISBN: | 9789814329644 9814329649 1283234866 9781283234863 9786613234865 6613234869 |
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| 245 | 1 | 0 | |6 880-01 |a Pseudo-Riemannian geometry, [delta]-invariants and applications / |c Bang-Yen Chen. |
| 246 | 3 | |a Pseudo-Riemannian geometry, d-invariants and applications | |
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| 505 | 0 | |a 1. Pseudo-Riemannian manifolds. 1.1. Symmetric bilinear forms and scalar products. 1.2. Pseudo-Riemannian manifolds. 1.3. Physical interpretations of pseudo-Riemannian manifolds. 1.4. Levi-Civita connection. 1.5. Parallel translation. 1.6. Riemann curvature tensor. 1.7. Sectional, Ricci and scalar curvatures. 1.8. Indefinite real space forms. 1.9. Lie derivative, gradient, Hessian and Laplacian. 1.10. Weyl conformal curvature tensor -- 2. Basics on pseudo-Riemannian submanifolds. 2.1. Isometric immersions. 2.2. Cartan-Janet's and Nash's embedding theorems. 2.3. Gauss' formula and second fundamental form. 2.4. Weingarten's formula and normal connection. 2.5. Shape operator of pseudo-Riemannian submanifolds. 2.6. Fundamental equations of Gauss, Codazzi and Ricci. 2.7. Fundamental theorems of submanifolds. 2.8. A reduction theorem of Erbacher-Magid. 2.9. Two basic formulas for submanifolds in E[symbol]. 2.10. Relationship between squared mean curvature and Ricci curvature. 2.11. Relationship between shape operator and Ricci curvature. 2.12. Cartan's structure equations -- 3. Special pseudo-Riemannian submanifolds. 3.1. Totally geodesic submanifolds. 3.2. Parallel submanifolds of (indefinite) real space forms. 3.3. Totally umbilical submanifolds. 3.4. Totally umbilical submanifolds of S[symbol] (1) and H[symbol] ( -1). 3.5. Pseudo-umbilical submanifolds of E[symbol]. 3.6. Pseudo-umbilical submanifolds of S[symbol] (1) and H[symbol] ( -1). 3.7. Minimal Lorentz surfaces in indefinite real space forms. 3.8. Marginally trapped surfaces and black holes. 3.9. Quasi-minimal surfaces in indefinite space forms -- 4. Warped products and twisted products. 4.1. Basics of warped products. 4.2. Curvature of warped products. 4.3. Warped product immersions. 4.4. Twisted products. 4.5. Double-twisted products and their characterization -- 5. Robertson-Walker spacetimes. 5.1. Cosmology, Robertson-Walker spacetimes and Einstein's field equations. 5.2. Basic properties of Robertson-Walker spacetimes. 5.3. Totally geodesic submanifolds of RW spacetimes. 5.4. Parallel submanifolds of RW spacetimes. 5.5. Totally umbilical submanifolds of RW spacetimes. 5.6. Hypersurfaces of constant curvature in RW spacetimes. 5.7. Realization of RW spacetimes in pseudo-Euclidean spaces. | |
| 520 | |a The first part of this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold theory. A number of recent results on pseudo-Riemannian submanifolds are also included. The second part of this book is on [symbol]-invariants, which was introduced in the early 1990s by the author. The famous Nash embedding theorem published in 1956 was aimed for, in the hope that if Riemannian manifolds could be regarded as Riemannian submanifolds, this would then yield the opportunity to use extrinsic help. However, this hope had not been materialized as pointed out by M. Gromov in his 1985 article published in Asterisque. The main reason for this is the lack of control of the extrinsic invariants of the submanifolds by known intrinsic invariants. In order to overcome such difficulties, as well as to provide answers for an open question on minimal immersions, the author introduced in the early 1990s new types of Riemannian invariants, known as [symbol]-invariants, which are very different in nature from the classical Ricci and scalar curvatures. At the same time he was able to establish general optimal relations between [symbol]-invariants and the main extrinsic invariants. Since then many new results concerning these [symbol]-invariants have been obtained by many geometers. The second part of this book is to provide an extensive and comprehensive survey over this very active field of research done during the last two decades. | ||
| 588 | 0 | |a Print version record. | |
| 546 | |a English. | ||
| 650 | 0 | |a Submanifolds. |0 http://id.loc.gov/authorities/subjects/sh85129484 | |
| 650 | 0 | |a Riemannian manifolds. |0 http://id.loc.gov/authorities/subjects/sh85114045 | |
| 650 | 0 | |a Geometry, Riemannian. |0 http://id.loc.gov/authorities/subjects/sh85054159 | |
| 650 | 0 | |a Invariants. |0 http://id.loc.gov/authorities/subjects/sh85067665 | |
| 650 | 6 | |a Sous-variétés (Mathématiques) | |
| 650 | 6 | |a Variétés de Riemann. | |
| 650 | 6 | |a Géométrie de Riemann. | |
| 650 | 6 | |a Invariants. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Differential. |2 bisacsh | |
| 650 | 7 | |a Geometry, Riemannian |2 fast | |
| 650 | 7 | |a Invariants |2 fast | |
| 650 | 7 | |a Riemannian manifolds |2 fast | |
| 650 | 7 | |a Submanifolds |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Chen, Bang-yen. |t Pseudo-Riemannian geometry, [delta]-invariants and applications. |d Singapore : World Scientific, ©2011 |z 9789814329637 |w (OCoLC)728077572 |
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| contents | 1. Pseudo-Riemannian manifolds. 1.1. Symmetric bilinear forms and scalar products. 1.2. Pseudo-Riemannian manifolds. 1.3. Physical interpretations of pseudo-Riemannian manifolds. 1.4. Levi-Civita connection. 1.5. Parallel translation. 1.6. Riemann curvature tensor. 1.7. Sectional, Ricci and scalar curvatures. 1.8. Indefinite real space forms. 1.9. Lie derivative, gradient, Hessian and Laplacian. 1.10. Weyl conformal curvature tensor -- 2. Basics on pseudo-Riemannian submanifolds. 2.1. Isometric immersions. 2.2. Cartan-Janet's and Nash's embedding theorems. 2.3. Gauss' formula and second fundamental form. 2.4. Weingarten's formula and normal connection. 2.5. Shape operator of pseudo-Riemannian submanifolds. 2.6. Fundamental equations of Gauss, Codazzi and Ricci. 2.7. Fundamental theorems of submanifolds. 2.8. A reduction theorem of Erbacher-Magid. 2.9. Two basic formulas for submanifolds in E[symbol]. 2.10. Relationship between squared mean curvature and Ricci curvature. 2.11. Relationship between shape operator and Ricci curvature. 2.12. Cartan's structure equations -- 3. Special pseudo-Riemannian submanifolds. 3.1. Totally geodesic submanifolds. 3.2. Parallel submanifolds of (indefinite) real space forms. 3.3. Totally umbilical submanifolds. 3.4. Totally umbilical submanifolds of S[symbol] (1) and H[symbol] ( -1). 3.5. Pseudo-umbilical submanifolds of E[symbol]. 3.6. Pseudo-umbilical submanifolds of S[symbol] (1) and H[symbol] ( -1). 3.7. Minimal Lorentz surfaces in indefinite real space forms. 3.8. Marginally trapped surfaces and black holes. 3.9. Quasi-minimal surfaces in indefinite space forms -- 4. Warped products and twisted products. 4.1. Basics of warped products. 4.2. Curvature of warped products. 4.3. Warped product immersions. 4.4. Twisted products. 4.5. Double-twisted products and their characterization -- 5. Robertson-Walker spacetimes. 5.1. Cosmology, Robertson-Walker spacetimes and Einstein's field equations. 5.2. Basic properties of Robertson-Walker spacetimes. 5.3. Totally geodesic submanifolds of RW spacetimes. 5.4. Parallel submanifolds of RW spacetimes. 5.5. Totally umbilical submanifolds of RW spacetimes. 5.6. Hypersurfaces of constant curvature in RW spacetimes. 5.7. Realization of RW spacetimes in pseudo-Euclidean spaces. |
| ctrlnum | (OCoLC)754793931 |
| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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code="a">Includes bibliographical references (pages 439-462) and indexes.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">1. Pseudo-Riemannian manifolds. 1.1. Symmetric bilinear forms and scalar products. 1.2. Pseudo-Riemannian manifolds. 1.3. Physical interpretations of pseudo-Riemannian manifolds. 1.4. Levi-Civita connection. 1.5. Parallel translation. 1.6. Riemann curvature tensor. 1.7. Sectional, Ricci and scalar curvatures. 1.8. Indefinite real space forms. 1.9. Lie derivative, gradient, Hessian and Laplacian. 1.10. Weyl conformal curvature tensor -- 2. Basics on pseudo-Riemannian submanifolds. 2.1. Isometric immersions. 2.2. Cartan-Janet's and Nash's embedding theorems. 2.3. Gauss' formula and second fundamental form. 2.4. Weingarten's formula and normal connection. 2.5. Shape operator of pseudo-Riemannian submanifolds. 2.6. Fundamental equations of Gauss, Codazzi and Ricci. 2.7. Fundamental theorems of submanifolds. 2.8. A reduction theorem of Erbacher-Magid. 2.9. Two basic formulas for submanifolds in E[symbol]. 2.10. Relationship between squared mean curvature and Ricci curvature. 2.11. Relationship between shape operator and Ricci curvature. 2.12. Cartan's structure equations -- 3. Special pseudo-Riemannian submanifolds. 3.1. Totally geodesic submanifolds. 3.2. Parallel submanifolds of (indefinite) real space forms. 3.3. Totally umbilical submanifolds. 3.4. Totally umbilical submanifolds of S[symbol] (1) and H[symbol] ( -1). 3.5. Pseudo-umbilical submanifolds of E[symbol]. 3.6. Pseudo-umbilical submanifolds of S[symbol] (1) and H[symbol] ( -1). 3.7. Minimal Lorentz surfaces in indefinite real space forms. 3.8. Marginally trapped surfaces and black holes. 3.9. Quasi-minimal surfaces in indefinite space forms -- 4. Warped products and twisted products. 4.1. Basics of warped products. 4.2. Curvature of warped products. 4.3. Warped product immersions. 4.4. Twisted products. 4.5. Double-twisted products and their characterization -- 5. Robertson-Walker spacetimes. 5.1. Cosmology, Robertson-Walker spacetimes and Einstein's field equations. 5.2. Basic properties of Robertson-Walker spacetimes. 5.3. Totally geodesic submanifolds of RW spacetimes. 5.4. Parallel submanifolds of RW spacetimes. 5.5. Totally umbilical submanifolds of RW spacetimes. 5.6. Hypersurfaces of constant curvature in RW spacetimes. 5.7. Realization of RW spacetimes in pseudo-Euclidean spaces.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The first part of this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold theory. A number of recent results on pseudo-Riemannian submanifolds are also included. The second part of this book is on [symbol]-invariants, which was introduced in the early 1990s by the author. The famous Nash embedding theorem published in 1956 was aimed for, in the hope that if Riemannian manifolds could be regarded as Riemannian submanifolds, this would then yield the opportunity to use extrinsic help. However, this hope had not been materialized as pointed out by M. Gromov in his 1985 article published in Asterisque. The main reason for this is the lack of control of the extrinsic invariants of the submanifolds by known intrinsic invariants. In order to overcome such difficulties, as well as to provide answers for an open question on minimal immersions, the author introduced in the early 1990s new types of Riemannian invariants, known as [symbol]-invariants, which are very different in nature from the classical Ricci and scalar curvatures. At the same time he was able to establish general optimal relations between [symbol]-invariants and the main extrinsic invariants. Since then many new results concerning these [symbol]-invariants have been obtained by many geometers. 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| id | ZDB-4-EBA-ocn754793931 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:18:01Z |
| institution | BVB |
| isbn | 9789814329644 9814329649 1283234866 9781283234863 9786613234865 6613234869 |
| language | English |
| oclc_num | 754793931 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xxxii, 477 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Chen, Bang-yen. 880-01 Pseudo-Riemannian geometry, [delta]-invariants and applications / Bang-Yen Chen. Pseudo-Riemannian geometry, d-invariants and applications Singapore : World Scientific, ©2011. 1 online resource (xxxii, 477 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 439-462) and indexes. 1. Pseudo-Riemannian manifolds. 1.1. Symmetric bilinear forms and scalar products. 1.2. Pseudo-Riemannian manifolds. 1.3. Physical interpretations of pseudo-Riemannian manifolds. 1.4. Levi-Civita connection. 1.5. Parallel translation. 1.6. Riemann curvature tensor. 1.7. Sectional, Ricci and scalar curvatures. 1.8. Indefinite real space forms. 1.9. Lie derivative, gradient, Hessian and Laplacian. 1.10. Weyl conformal curvature tensor -- 2. Basics on pseudo-Riemannian submanifolds. 2.1. Isometric immersions. 2.2. Cartan-Janet's and Nash's embedding theorems. 2.3. Gauss' formula and second fundamental form. 2.4. Weingarten's formula and normal connection. 2.5. Shape operator of pseudo-Riemannian submanifolds. 2.6. Fundamental equations of Gauss, Codazzi and Ricci. 2.7. Fundamental theorems of submanifolds. 2.8. A reduction theorem of Erbacher-Magid. 2.9. Two basic formulas for submanifolds in E[symbol]. 2.10. Relationship between squared mean curvature and Ricci curvature. 2.11. Relationship between shape operator and Ricci curvature. 2.12. Cartan's structure equations -- 3. Special pseudo-Riemannian submanifolds. 3.1. Totally geodesic submanifolds. 3.2. Parallel submanifolds of (indefinite) real space forms. 3.3. Totally umbilical submanifolds. 3.4. Totally umbilical submanifolds of S[symbol] (1) and H[symbol] ( -1). 3.5. Pseudo-umbilical submanifolds of E[symbol]. 3.6. Pseudo-umbilical submanifolds of S[symbol] (1) and H[symbol] ( -1). 3.7. Minimal Lorentz surfaces in indefinite real space forms. 3.8. Marginally trapped surfaces and black holes. 3.9. Quasi-minimal surfaces in indefinite space forms -- 4. Warped products and twisted products. 4.1. Basics of warped products. 4.2. Curvature of warped products. 4.3. Warped product immersions. 4.4. Twisted products. 4.5. Double-twisted products and their characterization -- 5. Robertson-Walker spacetimes. 5.1. Cosmology, Robertson-Walker spacetimes and Einstein's field equations. 5.2. Basic properties of Robertson-Walker spacetimes. 5.3. Totally geodesic submanifolds of RW spacetimes. 5.4. Parallel submanifolds of RW spacetimes. 5.5. Totally umbilical submanifolds of RW spacetimes. 5.6. Hypersurfaces of constant curvature in RW spacetimes. 5.7. Realization of RW spacetimes in pseudo-Euclidean spaces. The first part of this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold theory. A number of recent results on pseudo-Riemannian submanifolds are also included. The second part of this book is on [symbol]-invariants, which was introduced in the early 1990s by the author. The famous Nash embedding theorem published in 1956 was aimed for, in the hope that if Riemannian manifolds could be regarded as Riemannian submanifolds, this would then yield the opportunity to use extrinsic help. However, this hope had not been materialized as pointed out by M. Gromov in his 1985 article published in Asterisque. The main reason for this is the lack of control of the extrinsic invariants of the submanifolds by known intrinsic invariants. In order to overcome such difficulties, as well as to provide answers for an open question on minimal immersions, the author introduced in the early 1990s new types of Riemannian invariants, known as [symbol]-invariants, which are very different in nature from the classical Ricci and scalar curvatures. At the same time he was able to establish general optimal relations between [symbol]-invariants and the main extrinsic invariants. Since then many new results concerning these [symbol]-invariants have been obtained by many geometers. The second part of this book is to provide an extensive and comprehensive survey over this very active field of research done during the last two decades. Print version record. English. Submanifolds. http://id.loc.gov/authorities/subjects/sh85129484 Riemannian manifolds. http://id.loc.gov/authorities/subjects/sh85114045 Geometry, Riemannian. http://id.loc.gov/authorities/subjects/sh85054159 Invariants. http://id.loc.gov/authorities/subjects/sh85067665 Sous-variétés (Mathématiques) Variétés de Riemann. Géométrie de Riemann. Invariants. MATHEMATICS Geometry Differential. bisacsh Geometry, Riemannian fast Invariants fast Riemannian manifolds fast Submanifolds fast Print version: Chen, Bang-yen. Pseudo-Riemannian geometry, [delta]-invariants and applications. Singapore : World Scientific, ©2011 9789814329637 (OCoLC)728077572 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=389635 Volltext 245-01/(S Pseudo-Riemannian geometry, δ-invariants and applications / Bang-Yen Chen. 758-00 has work: Pseudo-Riemannian geometry, δ-invariants and applications (Text) https://id.oclc.org/worldcat/entity/E39PCGpdrTK7yM9xm3JT7cfMGd https://id.oclc.org/worldcat/ontology/hasWork |
| spellingShingle | Chen, Bang-yen Pseudo-Riemannian geometry, [delta]-invariants and applications / 1. Pseudo-Riemannian manifolds. 1.1. Symmetric bilinear forms and scalar products. 1.2. Pseudo-Riemannian manifolds. 1.3. Physical interpretations of pseudo-Riemannian manifolds. 1.4. Levi-Civita connection. 1.5. Parallel translation. 1.6. Riemann curvature tensor. 1.7. Sectional, Ricci and scalar curvatures. 1.8. Indefinite real space forms. 1.9. Lie derivative, gradient, Hessian and Laplacian. 1.10. Weyl conformal curvature tensor -- 2. Basics on pseudo-Riemannian submanifolds. 2.1. Isometric immersions. 2.2. Cartan-Janet's and Nash's embedding theorems. 2.3. Gauss' formula and second fundamental form. 2.4. Weingarten's formula and normal connection. 2.5. Shape operator of pseudo-Riemannian submanifolds. 2.6. Fundamental equations of Gauss, Codazzi and Ricci. 2.7. Fundamental theorems of submanifolds. 2.8. A reduction theorem of Erbacher-Magid. 2.9. Two basic formulas for submanifolds in E[symbol]. 2.10. Relationship between squared mean curvature and Ricci curvature. 2.11. Relationship between shape operator and Ricci curvature. 2.12. Cartan's structure equations -- 3. Special pseudo-Riemannian submanifolds. 3.1. Totally geodesic submanifolds. 3.2. Parallel submanifolds of (indefinite) real space forms. 3.3. Totally umbilical submanifolds. 3.4. Totally umbilical submanifolds of S[symbol] (1) and H[symbol] ( -1). 3.5. Pseudo-umbilical submanifolds of E[symbol]. 3.6. Pseudo-umbilical submanifolds of S[symbol] (1) and H[symbol] ( -1). 3.7. Minimal Lorentz surfaces in indefinite real space forms. 3.8. Marginally trapped surfaces and black holes. 3.9. Quasi-minimal surfaces in indefinite space forms -- 4. Warped products and twisted products. 4.1. Basics of warped products. 4.2. Curvature of warped products. 4.3. Warped product immersions. 4.4. Twisted products. 4.5. Double-twisted products and their characterization -- 5. Robertson-Walker spacetimes. 5.1. Cosmology, Robertson-Walker spacetimes and Einstein's field equations. 5.2. Basic properties of Robertson-Walker spacetimes. 5.3. Totally geodesic submanifolds of RW spacetimes. 5.4. Parallel submanifolds of RW spacetimes. 5.5. Totally umbilical submanifolds of RW spacetimes. 5.6. Hypersurfaces of constant curvature in RW spacetimes. 5.7. Realization of RW spacetimes in pseudo-Euclidean spaces. Submanifolds. http://id.loc.gov/authorities/subjects/sh85129484 Riemannian manifolds. http://id.loc.gov/authorities/subjects/sh85114045 Geometry, Riemannian. http://id.loc.gov/authorities/subjects/sh85054159 Invariants. http://id.loc.gov/authorities/subjects/sh85067665 Sous-variétés (Mathématiques) Variétés de Riemann. Géométrie de Riemann. Invariants. MATHEMATICS Geometry Differential. bisacsh Geometry, Riemannian fast Invariants fast Riemannian manifolds fast Submanifolds fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85129484 http://id.loc.gov/authorities/subjects/sh85114045 http://id.loc.gov/authorities/subjects/sh85054159 http://id.loc.gov/authorities/subjects/sh85067665 |
| title | Pseudo-Riemannian geometry, [delta]-invariants and applications / |
| title_alt | Pseudo-Riemannian geometry, d-invariants and applications |
| title_auth | Pseudo-Riemannian geometry, [delta]-invariants and applications / |
| title_exact_search | Pseudo-Riemannian geometry, [delta]-invariants and applications / |
| title_full | Pseudo-Riemannian geometry, [delta]-invariants and applications / Bang-Yen Chen. |
| title_fullStr | Pseudo-Riemannian geometry, [delta]-invariants and applications / Bang-Yen Chen. |
| title_full_unstemmed | Pseudo-Riemannian geometry, [delta]-invariants and applications / Bang-Yen Chen. |
| title_short | Pseudo-Riemannian geometry, [delta]-invariants and applications / |
| title_sort | pseudo riemannian geometry delta invariants and applications |
| topic | Submanifolds. http://id.loc.gov/authorities/subjects/sh85129484 Riemannian manifolds. http://id.loc.gov/authorities/subjects/sh85114045 Geometry, Riemannian. http://id.loc.gov/authorities/subjects/sh85054159 Invariants. http://id.loc.gov/authorities/subjects/sh85067665 Sous-variétés (Mathématiques) Variétés de Riemann. Géométrie de Riemann. Invariants. MATHEMATICS Geometry Differential. bisacsh Geometry, Riemannian fast Invariants fast Riemannian manifolds fast Submanifolds fast |
| topic_facet | Submanifolds. Riemannian manifolds. Geometry, Riemannian. Invariants. Sous-variétés (Mathématiques) Variétés de Riemann. Géométrie de Riemann. MATHEMATICS Geometry Differential. Geometry, Riemannian Invariants Riemannian manifolds Submanifolds |
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| work_keys_str_mv | AT chenbangyen pseudoriemanniangeometrydeltainvariantsandapplications AT chenbangyen pseudoriemanniangeometrydinvariantsandapplications |