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Differential Geometry in the Large

Seminar Lectures New York University 1946 and Stanford University 1956

Heinz Hopf (Autor)

Buch | Softcover

VIII, 192 Seiten

1989 | 2. Second Edition 1989
Springer Berlin (Verlag)
978-3-540-51497-8 (ISBN)

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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, .

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.

Erscheint lt. Verlag	9.8.1989
Reihe/Serie	Lecture Notes in Mathematics
Vorwort	S.S. Chern
Zusatzinfo	VIII, 192 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	320 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Curvature • Differentialgeometrie • Differential Geometry • differential geometry of surfaces • Differenzialgeometrie • Gaussian curvature • mean curvature • Riemannian manifold
ISBN-10	3-540-51497-X / 354051497X
ISBN-13	978-3-540-51497-8 / 9783540514978
Zustand	Neuware