內容簡介

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).

目錄

前言/序言

整體微分幾何

非常好的書，快遞給力

整體微分幾何

1854年德國數學傢黎曼（B. Riemann）在他的就職演講（Habilitationsschrift）中將高斯的理論推廣到n維空間，這就是黎曼幾何的誕生。其後許多數學傢，包括E. Beltrami， E. B. Christoffel，R. Lipschitz，L. Bianchi，T. Ricci開始沿著黎曼的思路進行研究。其中Bianchi是第一個將“微分幾何”作為書名的作者。

法國數學傢E·嘉當在微分幾何中強調聯絡的概念，建立瞭外微分的概念。這是整體微分幾何的奠基性的工作。隨後，中國數學傢陳省身從外微分的觀點齣發，推廣瞭麯麵上的高斯-博內定理。從此微分幾何成為現代數學不可缺少的領域。[

可以

書非常不錯

可以

書很好，慢慢看，我隻是為瞭點豆豆，還沒看