Differential Geometry: Bundles, Connections, Metrics and Curvature (Paperback)

Clifford Henry Taubes

  • 出版商: Oxford University
  • 出版日期: 2011-12-01
  • 售價: $2,600
  • 貴賓價: 9.5$2,470
  • 語言: 英文
  • 頁數: 312
  • 裝訂: Paperback
  • ISBN: 0199605874
  • ISBN-13: 9780199605873
  • 相關分類: 物理學 Physics
  • 無法訂購

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商品描述

Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects. 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 Kahler geometry. Differential Geometry 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. Helpfully, proofs are offered for almost all assertions throughout. All of the introductory material is presented in full and this is the only such source with the classical examples presented in detail.

商品描述(中文翻譯)

束、連結、度量和曲率是現代微分幾何和理論物理的「通用語言」。本書將為數學或理論物理的研究生提供這些概念的基礎知識。書中介紹了微分拓撲中使用的許多工具,並呈現了關於可微流形、光滑映射、微分形式、向量場、李群和格拉斯曼尼恩等基本結果。其他涵蓋的內容還包括關於測地線和雅可比場的基本定理、平坦連結的分類定理、特徵類的定義,以及對復雜和凱勒幾何的介紹。微分幾何使用了許多經典的例子和應用,特別是那些具有封閉形式表達的例子,以使抽象的概念變得具體。幸運的是,幾乎所有斷言都提供了證明。所有的入門材料都完整呈現,這是唯一一本詳細介紹經典例子的資源。