内容简介

This book is a study of an aspect of Elie Cartan's contribution to thequestion "What is geometry?"
In the last century two great generalizations of Euclidean geometry ap-peared. The first was the discovery of the non-Euclidean geometries. Thesewere organized into a coherent whole by Felix Klein, who recognized themas various examples of coset spaces G/H of Lie groups. In this book we refer to these latter as Klein geometries. The second generalization was Georg Riemann's discovery of what we now call Riemannian geometry. These two theories seemed largely incompatible with one other.1
In the early 1920s Elie Cartan, one of the pioneers of the theory of Lie groups, found that it was possible to obtain a common generalization of these theories, which he called espaces generalizes and we call Cartan geometries (see diagram).

目录

前言/序言

质量不错。好评

整体微分几何

书很好，慢慢看，我只是为了点豆豆，还没看

法国数学家E·嘉当在微分几何中强调联络的概念，建立了外微分的概念。这是整体微分几何的奠基性的工作。随后，中国数学家陈省身从外微分的观点出发，推广了曲面上的高斯-博内定理。从此微分几何成为现代数学不可缺少的领域。[

可以

可以

整体微分几何

可以

可以