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Differential geometry in the large : seminar lectures, New York University, 1946 and Stanford University, 1956

Author: Heinz Hopf; Shiing-Shen Chern
Publisher: Berlin ; New York : Springer-Verlag, 1983.
Series: Lecture notes in mathematics (Springer-Verlag), 1000.
Edition/Format:   Print book : EnglishView all editions and formats
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Additional Physical Format: Online version:
Hopf, Heinz, 1894-1971.
Differential geometry in the large.
Berlin ; New York : Springer-Verlag, 1983
(OCoLC)624998880
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Heinz Hopf; Shiing-Shen Chern
ISBN: 0387120041 9780387120041 3540120041 9783540120049
OCLC Number: 9622060
Description: vi, 184 pages : illustrations ; 25 cm.
Contents: Part ONE. I. Selected Topics in Geometry. 1. The Euler Characteristic and Related Topics ---
2. Selected Topics in Elementary Differential Geometry ---
3. The Isoperimetric Inequality and Related Inequalities ---
4. The Elementary Concept of Area and Volume ----
Part TWO. Differential Geometry in the Large. Introduction ----
1. Differential Geometry of Surfaces in the Small ---
2. Some General Remarks on Closed Surfaces in Differential Geometry ---
3. The Total Curvature (Curvatura Inteqra) of a Closed Surface with Riemannian Metric and Poincaréʹs Theorem on the Singularities of Fields of Line Elements ---
4. Hadamardʹs Characterization of the Ovaloids ---
5. Closed Surfaces with Constant Gauss Curvature (Hilbertʹs Method) --
Generalizations and Problems --
General Remarks on Weinqarten Surfaces ---
6. General Closed Surfaces of Genus O with Constant Mean Curvature --
Generalizations ---
7. Simple Closed Surfaces (of Arbitrary Genus) with Constant Mean Curvature --
Generalizations ---
8. The Congruence Theorem for Ovaloids ---
9. Singularities of Surfaces with Constant Negative Gauss Curvature.
Series Title: Lecture notes in mathematics (Springer-Verlag), 1000.
Responsibility: Heinz Hopf ; with a preface by S.S. Chern.

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