Geometric realizations of curvature:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
London
Imperial College Press
2012
|
| Schriftenreihe: | Imperial College Press advanced texts in mathematics
v. 6 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references and index 1. Introduction and statement of results. 1.1. Notational conventions. 1.2. Representation theory. 1.3. Affine structures. 1.4. Mixed structures. 1.5. Affine Kahler structures. 1.6. Riemannian structures. 1.7. Weyl geometry I. 1.8. Almost pseudo-hermitian geometry. 1.9. The Gray identity. 1.10. Kahler geometry in the Riemannian setting I. 1.11. Curvature Kahler-Weyl geometry. 1.12. The covariant derivative of the Kahler form I. 1.13. Hyper-hermitian geometry -- 2. Representation theory. 2.1. Modules for a group G. 2.2. Quadratic invariants. 2.3. Weyl's theory of invariants. 2.4. Some orthogonal modules. 2.5. Some unitary modules. 2.6. Compact Lie groups -- 3. Connections, curvature, and differential geometry. 3.1. Affine connections. 3.2. Equiaffine connections. 3.3. The Levi-Civita connection. 3.4. Complex geometry. 3.5. The Gray identity. 3.6. Kahler geometry in the Riemannian setting II -- - 4. Real affine geometry. 4.1. Decomposition of [symbol] and [symbol] as orthogonal modules. 4.2. The modules [symbol], S[symbol] and [symbol] in [symbol]. 4.3. The modules W[symbol], W[symbol] and W[symbol] in [symbol]. 4.4. Decomposition of [symbol] as a general linear module. 4.5. Geometric realizability of affine curvature operators. 4.6. Decomposition of [symbol] as an orthogonal module -- 5. Affine Kahler geometry. 5.1. Affine Kahler curvature tensor quadratic invariants. 5.2. The Ricci tensor for a Kahler affine connection. 5.3. Constructing affine (para)-Kahler manifolds. 5.4. Affine Kahler curvature operators. 5.5. Affine para-Kahler curvature operators. 5.6. Structure of [symbol] as a GL[symbol] module -- 6. Riemannian geometry. 6.1. The Riemann curvature tensor. 6.2. The Weyl conformal curvature tensor. 6.3. The Cauchy-Kovalevskaya theorem. 6.4. Geometric realizations of Riemann curvature tensors. 6.5. Weyl geometry II -- - 7. Complex Riemannian geometry. 7.1. The decomposition of [symbol] as modules over [symbol]. 7.2. The submodules of [symbol] arising from the Ricci tensors. 7.3. Para-hermitian and pseudo-hermitian geometry. 7.4. Almost para-hermitian and almost pseudo-hermitian geometry. 7.5. Kahler geometry in the Riemannian setting III. 7.6. Complex Weyl geometry. 7.7. The covariant derivative of the Kahler form II. A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are reviewed and presented in a clear, coherent form, including the latest developments and proofs. Even though many authors have worked in this area in recent years, many fundamental questions still remain unanswered. Many studies begin by first working purely algebraically and then later progressing onto the geometric setting and it has been found that many questions in differential geometry can be phrased as problems involving the geometric realization of curvature. Curvature decompositions are central to all investigations in this area. The authors present numerous results including the Singer-Thorpe decomposition, the Bokan decomposition, the Nikcevic decomposition, the Tricerri-Vanhecke decomposition, the Gray-Hervella decomposition and the De Smedt decomposition. They then proceed to draw appropriate geometric conclusions from these decompositions. The book organizes, in one coherent volume, the results of research completed by many different investigators over the past 30 years. Complete proofs are given of results that are often only outlined in the original publications. Whereas the original results are usually in the positive definite (Riemannian setting), here the authors extend the results to the pseudo-Riemannian setting and then further, in a complex framework, to para-Hermitian geometry as well. In addition to that, new results are obtained as well, making this an ideal text for anyone wishing to further their knowledge of the science of curvature |
| Beschreibung: | 1 Online-Ressource (ix, 252 p. :) |
| ISBN: | 1848167415 1848167423 9781848167414 9781848167421 |
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| 245 | 1 | 0 | |a Geometric realizations of curvature |c Miguel Brozos Vázquez, Peter B. Gilkey, Stana Nikcevic |
| 264 | 1 | |a London |b Imperial College Press |c 2012 | |
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| 490 | 0 | |a Imperial College Press advanced texts in mathematics |v v. 6 | |
| 500 | |a Includes bibliographical references and index | ||
| 500 | |a 1. Introduction and statement of results. 1.1. Notational conventions. 1.2. Representation theory. 1.3. Affine structures. 1.4. Mixed structures. 1.5. Affine Kahler structures. 1.6. Riemannian structures. 1.7. Weyl geometry I. 1.8. Almost pseudo-hermitian geometry. 1.9. The Gray identity. 1.10. Kahler geometry in the Riemannian setting I. 1.11. Curvature Kahler-Weyl geometry. 1.12. The covariant derivative of the Kahler form I. 1.13. Hyper-hermitian geometry -- 2. Representation theory. 2.1. Modules for a group G. 2.2. Quadratic invariants. 2.3. Weyl's theory of invariants. 2.4. Some orthogonal modules. 2.5. Some unitary modules. 2.6. Compact Lie groups -- 3. Connections, curvature, and differential geometry. 3.1. Affine connections. 3.2. Equiaffine connections. 3.3. The Levi-Civita connection. 3.4. Complex geometry. 3.5. The Gray identity. 3.6. Kahler geometry in the Riemannian setting II -- | ||
| 500 | |a - 4. Real affine geometry. 4.1. Decomposition of [symbol] and [symbol] as orthogonal modules. 4.2. The modules [symbol], S[symbol] and [symbol] in [symbol]. 4.3. The modules W[symbol], W[symbol] and W[symbol] in [symbol]. 4.4. Decomposition of [symbol] as a general linear module. 4.5. Geometric realizability of affine curvature operators. 4.6. Decomposition of [symbol] as an orthogonal module -- 5. Affine Kahler geometry. 5.1. Affine Kahler curvature tensor quadratic invariants. 5.2. The Ricci tensor for a Kahler affine connection. 5.3. Constructing affine (para)-Kahler manifolds. 5.4. Affine Kahler curvature operators. 5.5. Affine para-Kahler curvature operators. 5.6. Structure of [symbol] as a GL[symbol] module -- 6. Riemannian geometry. 6.1. The Riemann curvature tensor. 6.2. The Weyl conformal curvature tensor. 6.3. The Cauchy-Kovalevskaya theorem. 6.4. Geometric realizations of Riemann curvature tensors. 6.5. Weyl geometry II -- | ||
| 500 | |a - 7. Complex Riemannian geometry. 7.1. The decomposition of [symbol] as modules over [symbol]. 7.2. The submodules of [symbol] arising from the Ricci tensors. 7.3. Para-hermitian and pseudo-hermitian geometry. 7.4. Almost para-hermitian and almost pseudo-hermitian geometry. 7.5. Kahler geometry in the Riemannian setting III. 7.6. Complex Weyl geometry. 7.7. The covariant derivative of the Kahler form II. | ||
| 500 | |a A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are reviewed and presented in a clear, coherent form, including the latest developments and proofs. Even though many authors have worked in this area in recent years, many fundamental questions still remain unanswered. Many studies begin by first working purely algebraically and then later progressing onto the geometric setting and it has been found that many questions in differential geometry can be phrased as problems involving the geometric realization of curvature. Curvature decompositions are central to all investigations in this area. The authors present numerous results including the Singer-Thorpe decomposition, the Bokan decomposition, the Nikcevic decomposition, the Tricerri-Vanhecke decomposition, the Gray-Hervella decomposition and the De Smedt decomposition. They then proceed to draw appropriate geometric conclusions from these decompositions. The book organizes, in one coherent volume, the results of research completed by many different investigators over the past 30 years. Complete proofs are given of results that are often only outlined in the original publications. Whereas the original results are usually in the positive definite (Riemannian setting), here the authors extend the results to the pseudo-Riemannian setting and then further, in a complex framework, to para-Hermitian geometry as well. In addition to that, new results are obtained as well, making this an ideal text for anyone wishing to further their knowledge of the science of curvature | ||
| 650 | 7 | |a MATHEMATICS / Calculus |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Mathematical Analysis |2 bisacsh | |
| 650 | 4 | |a Curvature | |
| 650 | 4 | |a Geometry | |
| 650 | 0 | 7 | |a Riemannsche Geometrie |0 (DE-588)4128462-8 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Riemannsche Geometrie |0 (DE-588)4128462-8 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Gilkey, Peter B. |d 1946- |e Sonstige |0 (DE-588)1024266850 |4 oth | |
| 700 | 1 | |a Nikčević, Stana |e Sonstige |0 (DE-588)1024116883 |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804175624606056448 |
|---|---|
| any_adam_object | |
| author | Brozos-Vázquez, Miguel |
| author_GND | (DE-588)1025772156 (DE-588)1024266850 (DE-588)1024116883 |
| author_facet | Brozos-Vázquez, Miguel |
| author_role | aut |
| author_sort | Brozos-Vázquez, Miguel |
| author_variant | m b v mbv |
| building | Verbundindex |
| bvnumber | BV043157699 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)797852271 (DE-599)BVBBV043157699 |
| dewey-full | 515/.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.1 |
| dewey-search | 515/.1 |
| dewey-sort | 3515 11 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043157699 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:19:15Z |
| institution | BVB |
| isbn | 1848167415 1848167423 9781848167414 9781848167421 |
| language | English |
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| record_format | marc |
| series2 | Imperial College Press advanced texts in mathematics |
| spelling | Brozos-Vázquez, Miguel Verfasser (DE-588)1025772156 aut Geometric realizations of curvature Miguel Brozos Vázquez, Peter B. Gilkey, Stana Nikcevic London Imperial College Press 2012 1 Online-Ressource (ix, 252 p. :) txt rdacontent c rdamedia cr rdacarrier Imperial College Press advanced texts in mathematics v. 6 Includes bibliographical references and index 1. Introduction and statement of results. 1.1. Notational conventions. 1.2. Representation theory. 1.3. Affine structures. 1.4. Mixed structures. 1.5. Affine Kahler structures. 1.6. Riemannian structures. 1.7. Weyl geometry I. 1.8. Almost pseudo-hermitian geometry. 1.9. The Gray identity. 1.10. Kahler geometry in the Riemannian setting I. 1.11. Curvature Kahler-Weyl geometry. 1.12. The covariant derivative of the Kahler form I. 1.13. Hyper-hermitian geometry -- 2. Representation theory. 2.1. Modules for a group G. 2.2. Quadratic invariants. 2.3. Weyl's theory of invariants. 2.4. Some orthogonal modules. 2.5. Some unitary modules. 2.6. Compact Lie groups -- 3. Connections, curvature, and differential geometry. 3.1. Affine connections. 3.2. Equiaffine connections. 3.3. The Levi-Civita connection. 3.4. Complex geometry. 3.5. The Gray identity. 3.6. Kahler geometry in the Riemannian setting II -- - 4. Real affine geometry. 4.1. Decomposition of [symbol] and [symbol] as orthogonal modules. 4.2. The modules [symbol], S[symbol] and [symbol] in [symbol]. 4.3. The modules W[symbol], W[symbol] and W[symbol] in [symbol]. 4.4. Decomposition of [symbol] as a general linear module. 4.5. Geometric realizability of affine curvature operators. 4.6. Decomposition of [symbol] as an orthogonal module -- 5. Affine Kahler geometry. 5.1. Affine Kahler curvature tensor quadratic invariants. 5.2. The Ricci tensor for a Kahler affine connection. 5.3. Constructing affine (para)-Kahler manifolds. 5.4. Affine Kahler curvature operators. 5.5. Affine para-Kahler curvature operators. 5.6. Structure of [symbol] as a GL[symbol] module -- 6. Riemannian geometry. 6.1. The Riemann curvature tensor. 6.2. The Weyl conformal curvature tensor. 6.3. The Cauchy-Kovalevskaya theorem. 6.4. Geometric realizations of Riemann curvature tensors. 6.5. Weyl geometry II -- - 7. Complex Riemannian geometry. 7.1. The decomposition of [symbol] as modules over [symbol]. 7.2. The submodules of [symbol] arising from the Ricci tensors. 7.3. Para-hermitian and pseudo-hermitian geometry. 7.4. Almost para-hermitian and almost pseudo-hermitian geometry. 7.5. Kahler geometry in the Riemannian setting III. 7.6. Complex Weyl geometry. 7.7. The covariant derivative of the Kahler form II. A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are reviewed and presented in a clear, coherent form, including the latest developments and proofs. Even though many authors have worked in this area in recent years, many fundamental questions still remain unanswered. Many studies begin by first working purely algebraically and then later progressing onto the geometric setting and it has been found that many questions in differential geometry can be phrased as problems involving the geometric realization of curvature. Curvature decompositions are central to all investigations in this area. The authors present numerous results including the Singer-Thorpe decomposition, the Bokan decomposition, the Nikcevic decomposition, the Tricerri-Vanhecke decomposition, the Gray-Hervella decomposition and the De Smedt decomposition. They then proceed to draw appropriate geometric conclusions from these decompositions. The book organizes, in one coherent volume, the results of research completed by many different investigators over the past 30 years. Complete proofs are given of results that are often only outlined in the original publications. Whereas the original results are usually in the positive definite (Riemannian setting), here the authors extend the results to the pseudo-Riemannian setting and then further, in a complex framework, to para-Hermitian geometry as well. In addition to that, new results are obtained as well, making this an ideal text for anyone wishing to further their knowledge of the science of curvature MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Curvature Geometry Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Riemannsche Geometrie (DE-588)4128462-8 s 1\p DE-604 Gilkey, Peter B. 1946- Sonstige (DE-588)1024266850 oth Nikčević, Stana Sonstige (DE-588)1024116883 oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=457216 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Brozos-Vázquez, Miguel Geometric realizations of curvature MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Curvature Geometry Riemannsche Geometrie (DE-588)4128462-8 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4128462-8 (DE-588)4012248-7 |
| title | Geometric realizations of curvature |
| title_auth | Geometric realizations of curvature |
| title_exact_search | Geometric realizations of curvature |
| title_full | Geometric realizations of curvature Miguel Brozos Vázquez, Peter B. Gilkey, Stana Nikcevic |
| title_fullStr | Geometric realizations of curvature Miguel Brozos Vázquez, Peter B. Gilkey, Stana Nikcevic |
| title_full_unstemmed | Geometric realizations of curvature Miguel Brozos Vázquez, Peter B. Gilkey, Stana Nikcevic |
| title_short | Geometric realizations of curvature |
| title_sort | geometric realizations of curvature |
| topic | MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Curvature Geometry Riemannsche Geometrie (DE-588)4128462-8 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | MATHEMATICS / Calculus MATHEMATICS / Mathematical Analysis Curvature Geometry Riemannsche Geometrie Differentialgeometrie |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=457216 |
| work_keys_str_mv | AT brozosvazquezmiguel geometricrealizationsofcurvature AT gilkeypeterb geometricrealizationsofcurvature AT nikcevicstana geometricrealizationsofcurvature |