Aspects of differential geometry III
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| Главные авторы: | , , , , |
|---|---|
| Формат: | Livre papier |
| Язык: | Anglais |
| Опубликовано: |
[San Rafael, California] :
Morgan & Claypool Publishers
C 2017.
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| Серии: | Synthesis lectures on mathematics and statistics
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| Предметы: | |
| Примечание: |
"Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book III is aimed at the first-year graduate level but is certainly accessible to advanced undergraduates. It deals with invariance theory and discusses invariants both of Weyl and not of Weyl type; the Chern-Gauss-Bonnet formula is treated from this point of view. Homothety homogeneity, local homogeneity, stability theorems, and Walker geometry are discussed. Ricci solitons are presented in the contexts of Riemannian, Lorentzian, and affine geometry."--Back cover Autres auteurs : JeongHyeong Park,... Ramón Vázquez-Lorenzo,... |
| Autres localisations: | Voir dans le Sudoc |
Оглавление:
- 9. Invariance theory
- 9.1 Review of affine and Riemannian geometry
- 9.2 Invariance theory in the Riemannian setting
- 9.3 The Chern-Gauss-Bonnet formula
- 9.4 Pseudo-Kähler manifolds
- 9.5 VSI manifolds
- 9.6 Invariants that are not of Weyl type
- 10. Homothety homogeneity and local homogeneity
- 10.1 Introduction
- 10.2 Classification results
- 10.3 Completeness
- 10.4 3-Dimensional Walker Lorentzian manifolds I: Curvature homogeneity
- 10.5 Walker Lorentzian manifolds II: Homothety curvature homogeneity
- 10.6 Stability
- 10.7 Locally homogeneous metric g-structures
- 11. Ricci solitons
- 11.1 Introduction
- 11.2 Riemanian homogeneous Ricci almost solitons
- 11.3 Lorentzian homogeneous gradient Ricci solitons
- 11.4 Riemannian locally conformally flat gradient Ricci solitons
- 11.5 Lorentzian locally conformally flat gradient Ricci solitons
- 11.6 Neutral signature self-dual gradient Ricci almost solitons
- Bibliography
- Authors' biographies
- Index