Differential Geometry in the Large : Seminar Lectures New York University 1946 and Stanford University 1956 / by Heinz Hopf.

Format:

Book

Author/Creator:

Hopf, Heinz, 1894-1971, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1000.

Lecture Notes in Mathematics, 0075-8434 ; 1000

Language:

English

Subjects (All):

Global differential geometry.

Differential Geometry.

Local Subjects:

Differential Geometry.

Physical Description:

1 online resource (VIII, 192 pages).

Edition:

Second Edition.

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1989.

System Details:

text file PDF

Summary:

These notes consist of two parts: Selected in York 1) Geometry, New 1946, Topics University Notes Peter Lax. by Differential in the 2) Lectures on Stanford Geometry Large, 1956, Notes J.W. University by Gray. are here with no essential They reproduced change. Heinz was a mathematician who mathema- Hopf recognized important tical ideas and new mathematical cases. In the phenomena through special the central idea the of a or difficulty problem simplest background is becomes clear. in this fashion a crystal Doing geometry usually lead serious allows this to to - joy. Hopf's great insight approach for most of the in these notes have become the st- thematics, topics I will to mention a of further try ting-points important developments. few. It is clear from these notes that laid the on Hopf emphasis po- differential Most of the results in smooth differ- hedral geometry. whose is both t1al have understanding geometry polyhedral counterparts, works I wish to mention and recent important challenging. Among those of Robert on which is much in the Connelly rigidity, very spirit R. and in - of these notes (compare Connelly, Conjectures questions open International of Mathematicians, H- of gidity, Proceedings Congress sinki volume 1, 407-414) 1978, .

Contents:

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 Poincaré'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.

Other Format:

Printed edition:

ISBN:

9783540394822

Access Restriction:

Restricted for use by site license.