Differential Geometry: Manifolds, Curves, and Surfaces
Differential Geometry: Manifolds, Curves, and Surfaces
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发表时间：
1987-11
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通讯作者：
M. Berger;Bernard Gostiaux;S. Levy
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作者：
M. Berger;Bernard Gostiaux;S. Levy
这本书是对现代微分几何的介绍。作者开始与必要的工具，从分析和拓扑学，包括萨尔德定理，德拉姆上同调，微积分流形，和一个度理论。用曲线和曲面的例子说明和扩展了一般理论。特别是，这本书包含了经典的局部和全球理论的表面，包括基本形式，曲率，高斯-邦纳公式，测地线，和极小曲面。
This book is an introduction to modern differential geometry. The authors begin with the necessary tools from analysis and topology, including Sard's theorem, de Rham cohomology, calculus on manifolds, and a degree theory. The general theory is illustrated and expanded using the examples of curves and surfaces. In particular, the book contains the classical local and global theory of surfaces, including the fundamental forms, curvature, the Gauss-Bonnet formula, geodesics, and minimal surfaces.