Differential Geometry in the Large

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Beschreibung

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 (cf. Connelly, Conjectures questions open International of Mathematicians, H- of gidity, Proceedings Congress sinki vol. 1, 407-414) 1978, .

Zusammenfassung

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Erscheinungsjahr:	1989
Fachbereich:	Geometrie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	200
Reihe:	Lecture Notes in Mathematics
Inhalt:	viii 192 S.
ISBN-13:	9783540514978
ISBN-10:	354051497X
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Hopf, Heinz
Auflage:	2nd ed. 1989
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg Lecture Notes in Mathematics
Maße:	235 x 155 x 12 mm
Von/Mit:	Heinz Hopf
Erscheinungsdatum:	09.08.1989
Gewicht:	0,312 kg

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