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Aspects of differential geometry II /

Bibliographic Details
Main Authors:	Gilkey, Peter B. (Author), Park, Jeonghyeong (Author), Vázquez-Lorenzo, Ramón (Author)
Format:	eBook
Language:	English
Published:	San Rafael, California (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool, 2015.
Series:	Synthesis lectures on mathematics and statistics ; # 16.
Subjects:	Geometry, Differential. Chern classes Clifford algebra Jacobi operator Kahler geometry Levi-Civita connection Lie algebra Lie group Peter-Weyl Theorem Riemannian geometry connection de Rham cohomology geodesic pseudo-Riemannian geometry sheaf cohomology simplicial cohomology singular cohomology symmetric space volume of geodesic balls Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

4. Additional topics in Riemannian geometry
4.1 Curves and surfaces in Rn given by ODEs
4.2 Volume of geodesic balls
4.3 Holomorphic geometry
4.4 Kahler geometry
5. de Rham cohomology
5.1 Basic properties of de Rham cohomology
5.2 Clifford algebras
5.3 The Hodge decomposition theorem
5.4 Characteristic classes
6. Lie groups
6.1 Basic concepts
6.2 Lie algebras
6.3 The exponential function of a matrix group
6.4 The classical groups
6.5 Representations of a compact lie group
6.6 Bi-invariant pseudo-Riemannian metrics
6.7 The killing form
6.8 The classical groups in low dimensions
6.9 The cohomology of compact lie groups
6.10 The cohomology of the unitary group
7. Homogeneous spaces and symmetric spaces
7.1 Smooth structures on coset spaces
7.2 The isometry group
7.3 The lie derivative and killing vector fieldS
7.4 Homogeneous pseudo-Riemannian manifolds
7.5 Local symmetric spaces
7.6 The global geometry of symmetric spaces
8. Other cohomology theories
8.1 Homological algebra
8.2 Simplicial cohomology
8.3 Singular cohomology
8.4 Sheaf cohomology
Bibliography
Authors' biographies
Index.