Differential geometry in the large: Seminar lectures, New York University, 1946 and Stanford University, 1956
Differential geometry in the large: Seminar lectures, New York University, 1946 and Stanford University, 1956
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发表时间：
1983
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通讯作者：
H. Hopf
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作者：
H. Hopf
选择几何主题。-欧拉特性及相关主题。-《初等微分几何选题》。-等周不等式及相关不等式。-面积和体积的基本概念。-微分几何的大。-小曲面的微分几何。微分几何中关于闭曲面的一些一般注意事项。用黎曼度规和关于线元场奇点的庞加莱定理研究封闭曲面的总曲率（曲率积分）。——Hadamard对卵圆体的描述。-具有恒定高斯曲率的封闭曲面（希尔伯特方法）-推广和问题-关于温卡滕曲面的一般注释-具有常平均曲率的O属的一般闭曲面-推广。-具有恒定平均曲率的简单闭曲面（任意属）-推广。-卵圆的同余定理。-具有恒定负高斯曲率曲面的奇异性。
Selected Topics in Geometry.- The Euler Characteristic and Related Topics.- Selected Topics in Elementary Differential Geometry.- The Isoperimetric Inequality and Related Inequalities.- The Elementary Concept of Area and Volume.- Differential Geometry in the Large.- Differential Geometry of Surfaces in the Small.- Some General Remarks on Closed Surfaces in Differential Geometry.- The Total Curvature (Curvatura Inteqra) of a Closed Surface with Riemannian Metric and Poincare's Theorem on the Singularities of Fields of Line Elements.- Hadamard's Characterization of the Ovaloids.- Closed Surfaces with Constant Gauss Curvature (Hilbert's Method) - Generalizations and Problems - General Remarks on Weinqarten Surfaces.- General Closed Surfaces of Genus O with Constant Mean Curvature - Generalizations.- Simple Closed Surfaces (of Arbitrary Genus) with Constant Mean Curvature - Generalizations.- The Congruence Theorem for Ovaloids.- Singularities of Surfaces with Constant Negative Gauss Curvature.