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Some Global Theorems on Hypersurfaces

Published online by Cambridge University Press:  20 November 2018

Chuan-Chih Hsiung
Chuan-Chih Hsiung*
Affiliation:
Lehigh University
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The purpose of this paper is to establish the following theorems, which were obtained by Hopf and Voss in their joint paper (2) for the case where n = 2.

THEOREM 1. Let Vn, V*n be two closed orientable hyper surfaces twice differ entiably imbedded in a Euclidean space En+l of dimension n + 1 ≥ 3.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 5 - 14
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Blaschke, W., Vorlesungen über Differentialgeometrie (Vol. 1, 3rd ed., Berlin, 1930).Google Scholar
2. Hopf, H. and Voss, K., Ein Satz aus der Flächentheorie im Grossen, Archiv der Mathematik, 3 (1952), 187–192.Google Scholar
3. Hsiung, C. C., Some integral formulas for closed hyper surfaces, Math. Scandinavica, 2 (1954), 286–294.Google Scholar
4. Pólya, G. and Szegö, G., Isoperimetric inequalities in mathematical physics (Ann. Math. Studies, No. 42, Princeton, 1951).Google Scholar