Differential Geometry in the Large: Seminar Lectures New York University 1946 and Stanford University 1956

Front Matter....Pages N2-VII
Front Matter....Pages 1-1
The Euler Characteristic and Related Topics....Pages 3-29
Selected Topics in Elementary Differential Geometry....Pages 30-46
The Isoperimetric Inequality and Related Inequalities....Pages 47-57
The Elementary Concept of Area and Volume....Pages 58-75
Front Matter....Pages 77-80
Introduction....Pages 81-81
Differential Geometry of Surfaces in the Small [summary sketch]....Pages 82-99
Some General Remarks on Closed Surfaces in Differential Geometry....Pages 100-106
The Total Curvature (Curvatura Integra) of a Closed Surface with Riemannian Metric and Poincaré’s Theorem on the Singularities of Fields of Line Elements....Pages 107-118
Hadamard’s Characterization of the Ovaloids....Pages 119-122
Closed Surfaces with Constant Gauss Curvature (Hilbert’s Method)— Generalizations and Problems — General Remarks on Weingarten Surfaces....Pages 123-135
General Closed Surfaces of Genus O with Constant Mean Curvature - Generalizations....Pages 136-146
Simple Closed Surfaces (of Arbitrary Genus) with Constant Mean Curvature — Generalizations....Pages 147-162
The Congruence Theorem for Ovaloids....Pages 163-173
Singularities of Surfaces with Constant Negative Gauss Curvature....Pages 174-184
Back Matter....Pages 185-187