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Differential Geometry in the Large

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Cover of 'Differential Geometry in the Large'

Table of Contents

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    Book Overview
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    Chapter 1 The Euler Characteristic and Related Topics
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    Chapter 2 Selected Topics in Elementary Differential Geometry
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    Chapter 3 The Isoperimetric Inequality and Related Inequalities
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    Chapter 4 The Elementary Concept of Area and Volume
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    Chapter 5 Introduction
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    Chapter 6 Differential Geometry of Surfaces in the Small
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    Chapter 7 Some General Remarks on Closed Surfaces in Differential Geometry
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    Chapter 8 The Total Curvature (Curvatura Inteqra) of a Closed Surface with Riemannian Metric and Poincaré’s Theorem on the Singularities of Fields of Line Elements
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    Chapter 9 Hadamard’s Characterization of the Ovaloids
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    Chapter 10 Closed Surfaces with Constant Gauss Curvature (Hilbert’s Method) — Generalizations and Problems — General Remarks on Weinqarten Surfaces
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    Chapter 11 General Closed Surfaces of Genus O with Constant Mean Curvature — Generalizations
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    Chapter 12 Simple Closed Surfaces (of Arbitrary Genus) with Constant Mean Curvature — Generalizations
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    Chapter 13 The Congruence Theorem for Ovaloids
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    Chapter 14 Singularities of Surfaces with Constant Negative Gauss Curvature
Attention for Chapter 7: Some General Remarks on Closed Surfaces in Differential Geometry
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Chapter title
Some General Remarks on Closed Surfaces in Differential Geometry
Chapter number 7
Book title
Differential Geometry in the Large
Published by
Springer, Berlin, Heidelberg, January 1989
DOI 10.1007/3-540-39482-6_7
Book ISBNs
978-3-54-051497-8, 978-3-54-039482-2
Authors

Heinz Hopf, Hopf, Heinz

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