Differential Geometry: Bundles, Connections, Metrics and Curvature

丛 书 名：Oxford graduate texts in mathematics

版本说明：1

作     者：Clifford Henry Taubes 

I S B N：(纸本) 9780199605880 

出 版 社：Oxford University Press 

出 版 年：2011年

页      数：xiii, 298 p. ;页

主 题 词：bundles metrics curvature differential geometry theoretical physics differential topology differentiable manifolds smooth maps differential forms vector fields 

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

馆 藏 号：201251630...

摘      要：Bundles, connections, metrics, and curvature are the ‘lingua franca’ of modern differential geometry and theoretical physics. Many of the tools used in differential topology are introduced and the basic results about differentiable manifolds, smooth maps, differential forms, vector fields, Lie groups, and Grassmanians are all presented here. Other material covered includes the basic theorems about geodesics and Jacobi fields, the classification theorem for flat connections, the definition of characteristic classes, and also an introduction to complex and Kähler geometry. The book uses many of the classical examples from, and applications of, the subjects it covers, in particular those where closed form expressions are available, to bring abstract ideas to life.