The geometry of Hessian structures /:
The geometry of Hessian structures is a fascinating emerging field of research. It is in particular a very close relative of Kählerian geometry, and connected with many important pure mathematical branches such as affine differential geometry, homogeneous spaces and cohomology. The theory also finds...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Hackensack, N.J. :
World Scientific,
©2007.
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| Online-Zugang: | Volltext |
| Zusammenfassung: | The geometry of Hessian structures is a fascinating emerging field of research. It is in particular a very close relative of Kählerian geometry, and connected with many important pure mathematical branches such as affine differential geometry, homogeneous spaces and cohomology. The theory also finds deep relation to information geometry in applied mathematics. This systematic introduction to the subject first develops the fundamentals of Hessian structures on the basis of a certain pair of a flat connection and a Riemannian metric, and then describes these related fields as applications of the. |
| Beschreibung: | 1 online resource (xiv, 246 pages) |
| Bibliographie: | Includes bibliographical references (pages 237-241) and index. |
| ISBN: | 9789812707536 9812707530 |
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| 505 | 0 | |a Preface; Introduction; Contents; 1. Affine spaces and connections; 2. Hessian structures; 3. Curvatures for Hessian structures; 4. Regular convex cones; 5. Hessian structures and affine differential geometry; 6. Hessian structures and information geometry; 7. Cohomology on at manifolds; 8. Compact Hessian manifolds; 9. Symmetric spaces with invariant Hessian structures; 10. Homogeneous spaces with invariant Hessian structures; 11. Homogeneous spaces with invariant projectively at connections; Bibliography; Index. | |
| 520 | |a The geometry of Hessian structures is a fascinating emerging field of research. It is in particular a very close relative of Kählerian geometry, and connected with many important pure mathematical branches such as affine differential geometry, homogeneous spaces and cohomology. The theory also finds deep relation to information geometry in applied mathematics. This systematic introduction to the subject first develops the fundamentals of Hessian structures on the basis of a certain pair of a flat connection and a Riemannian metric, and then describes these related fields as applications of the. | ||
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| author | Shima, Hirohiko |
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| contents | Preface; Introduction; Contents; 1. Affine spaces and connections; 2. Hessian structures; 3. Curvatures for Hessian structures; 4. Regular convex cones; 5. Hessian structures and affine differential geometry; 6. Hessian structures and information geometry; 7. Cohomology on at manifolds; 8. Compact Hessian manifolds; 9. Symmetric spaces with invariant Hessian structures; 10. Homogeneous spaces with invariant Hessian structures; 11. Homogeneous spaces with invariant projectively at connections; Bibliography; Index. |
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| discipline | Mathematik |
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| id | ZDB-4-EBA-ocn172989118 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:16:08Z |
| institution | BVB |
| isbn | 9789812707536 9812707530 |
| language | English |
| oclc_num | 172989118 |
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| spelling | Shima, Hirohiko. http://id.loc.gov/authorities/names/no2007069178 The geometry of Hessian structures / Hirohiko Shima. Hessian structures Hackensack, N.J. : World Scientific, ©2007. 1 online resource (xiv, 246 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 237-241) and index. Print version record. Preface; Introduction; Contents; 1. Affine spaces and connections; 2. Hessian structures; 3. Curvatures for Hessian structures; 4. Regular convex cones; 5. Hessian structures and affine differential geometry; 6. Hessian structures and information geometry; 7. Cohomology on at manifolds; 8. Compact Hessian manifolds; 9. Symmetric spaces with invariant Hessian structures; 10. Homogeneous spaces with invariant Hessian structures; 11. Homogeneous spaces with invariant projectively at connections; Bibliography; Index. The geometry of Hessian structures is a fascinating emerging field of research. It is in particular a very close relative of Kählerian geometry, and connected with many important pure mathematical branches such as affine differential geometry, homogeneous spaces and cohomology. The theory also finds deep relation to information geometry in applied mathematics. This systematic introduction to the subject first develops the fundamentals of Hessian structures on the basis of a certain pair of a flat connection and a Riemannian metric, and then describes these related fields as applications of the. Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Homology theory. http://id.loc.gov/authorities/subjects/sh85061770 Homogeneous spaces. http://id.loc.gov/authorities/subjects/sh85061766 Manifolds (Mathematics) http://id.loc.gov/authorities/subjects/sh85080549 Géométrie différentielle. Homologie. Espaces homogènes. Variétés (Mathématiques) MATHEMATICS Geometry Differential. bisacsh Geometry, Differential fast Homogeneous spaces fast Homology theory fast Manifolds (Mathematics) fast has work: The geometry of Hessian structures (Text) https://id.oclc.org/worldcat/entity/E39PCGGGDD4vRGxpCkYmb7gyq3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Shima, Hirohiko. Geometry of Hessian structures. Hackensack, N.J. : World Scientific, ©2007 9812700315 9789812700315 (DLC) 2007298479 (OCoLC)167542989 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=203860 Volltext |
| spellingShingle | Shima, Hirohiko The geometry of Hessian structures / Preface; Introduction; Contents; 1. Affine spaces and connections; 2. Hessian structures; 3. Curvatures for Hessian structures; 4. Regular convex cones; 5. Hessian structures and affine differential geometry; 6. Hessian structures and information geometry; 7. Cohomology on at manifolds; 8. Compact Hessian manifolds; 9. Symmetric spaces with invariant Hessian structures; 10. Homogeneous spaces with invariant Hessian structures; 11. Homogeneous spaces with invariant projectively at connections; Bibliography; Index. Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Homology theory. http://id.loc.gov/authorities/subjects/sh85061770 Homogeneous spaces. http://id.loc.gov/authorities/subjects/sh85061766 Manifolds (Mathematics) http://id.loc.gov/authorities/subjects/sh85080549 Géométrie différentielle. Homologie. Espaces homogènes. Variétés (Mathématiques) MATHEMATICS Geometry Differential. bisacsh Geometry, Differential fast Homogeneous spaces fast Homology theory fast Manifolds (Mathematics) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85054146 http://id.loc.gov/authorities/subjects/sh85061770 http://id.loc.gov/authorities/subjects/sh85061766 http://id.loc.gov/authorities/subjects/sh85080549 |
| title | The geometry of Hessian structures / |
| title_alt | Hessian structures |
| title_auth | The geometry of Hessian structures / |
| title_exact_search | The geometry of Hessian structures / |
| title_full | The geometry of Hessian structures / Hirohiko Shima. |
| title_fullStr | The geometry of Hessian structures / Hirohiko Shima. |
| title_full_unstemmed | The geometry of Hessian structures / Hirohiko Shima. |
| title_short | The geometry of Hessian structures / |
| title_sort | geometry of hessian structures |
| topic | Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Homology theory. http://id.loc.gov/authorities/subjects/sh85061770 Homogeneous spaces. http://id.loc.gov/authorities/subjects/sh85061766 Manifolds (Mathematics) http://id.loc.gov/authorities/subjects/sh85080549 Géométrie différentielle. Homologie. Espaces homogènes. Variétés (Mathématiques) MATHEMATICS Geometry Differential. bisacsh Geometry, Differential fast Homogeneous spaces fast Homology theory fast Manifolds (Mathematics) fast |
| topic_facet | Geometry, Differential. Homology theory. Homogeneous spaces. Manifolds (Mathematics) Géométrie différentielle. Homologie. Espaces homogènes. Variétés (Mathématiques) MATHEMATICS Geometry Differential. Geometry, Differential Homogeneous spaces Homology theory |
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