Closed convex hypersurfaces with second fundamental form of constant curvature-Reference-Cited by-同舟云学术

Closed convex hypersurfaces with second fundamental form of constant curvature

Published:1972 Issue:1 Volume:35 Page:230-233
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Schneider Rolf

Abstract

It is shown that the Euclidean spheres are the only closed hypersurfaces in Euclidean space on which the second fundamental form defines a (nondegenerate) Riemannian metric of constant curvature.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1972-035-01/S0002-9939-1972-0307133-1/S0002-9939-1972-0307133-1.pdf

Reference9 articles.

1. Les surfaces qui admettent une seconde forme fondamentale donnée;Cartan, Élie;Bull. Sci. Math. (2),1943

2. Abhandlung zur Erlangung der W\"{u}rde eines Doktors der Mathematik der Eidgen\"{o}ssischen Technischen Hochschule Z\"{u}rich;Erard, Pierre Jean,1968

3. R. B. Gardner, Subscalar pairs of metrics with applications to rigidity and uniqueness of hypersurfaces with a non-degenerate second fundamental form (to appear).

4. Zur affinen Differentialgeometrie im Grossen. I;Schneider, Rolf;Math. Z.,1967

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