微分幾何 下載 mobi epub pdf 電子書 2025

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

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整體微分幾何

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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。[

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