Aspects of Differential Geometry III


Categories: ,
Author(s): Esteban Calviño-Louzao, Eduardo García-Río, Peter Gilkey

Series: Synthesis Lectures on Mathematics and Statistics

Publisher: Calviǫ-louzao, Esteban, Garca̕-ro̕, Eduardo, Gilkey, Peter, Morgan & Claypool, Park, Jeonghyeong, Vz̀quez-lorenzo, Ramn̤;Morgan & Claypool Publishers, Year: 2017

ISBN: 1627056866,9781627056861

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

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