Geometric Structures on Manifolds

eBook 미리보기

· 제목 : Geometric Structures on Manifolds (Paperback)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 기하학 > 기하학 일반
· ISBN : 9781470471989
· 쪽수 : 437쪽
· 출판일 : 2023-01-30

Part 1. Affine and projective geometry: Affine geometry
Projective geometry
Duality and non-Euclidean geometry
Convexity
Part 2. Geometric manifolds: Locally homogeneous geometric structures
Examples of geometric structures
Classification
Completeness
Part 3. Affine and projective structures: Affine structures on surfaces and the Euler characteristic
Affine Lie groups
Parallel volume and completeness
Hyperbolicity
Projective structures on surfaces
Complex-projective structures
Geometric structures on 3-manifolds
Appendices: Appendix A. Transformation groups
Appendix B. Affine connections
Appendix C. Representations of nilpotent groups
Appendix D. 4-dimensional filiform nilpotent Lie algebras
Appendix E. Semicontinuous functions
Appendix F. $\mathsf{SL}(2,\mathbb{C})$ and $O(3,1)$
Appendix G. Lagrangian foliations of symplectic manifolds
Bibliography
Index