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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Characterization of totally umbilical hypersurfaces


Author: Thomas Hasanis
Journal: Proc. Amer. Math. Soc. 81 (1981), 447-450
MSC: Primary 53C40; Secondary 53C20
MathSciNet review: 597660
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Abstract: This paper gives a sufficient condition for a complete hypersurface of a Riemannian manifold of constant curvature to be umbilical. The condition will be given by an inequality which is established between the length of the second fundamental tensor and the mean curvature.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0597660-X
Keywords: Second fundamental tensor, totally umbilical hypersurfaces
Article copyright: © Copyright 1981 American Mathematical Society