Aspects of Differential Geometry III
Aspects of Differential Geometry I（2017）
摘要
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 ChernGaussBonnet 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.
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关键词
lie algebra,geodesic,inverse function theorem,clifford algebra,riemannian geometry,lie group,green s theorem,symmetric space,connection,jacobi operator,peter weyl theorem,chern classes,levi civita connection,fubini s theorem,implicit function theorem,gauss bonnet theorem,sheaf cohomology,de rham cohomology,improper integrals,riemann integral
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