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COMPLETE WEINGARTEN HYPERSURFACES SATISFYING AN OKUMURA TYPE INEQUALITY
Published online by Cambridge University Press: 11 March 2019
Abstract
In this paper we deal with complete linear Weingarten hypersurfaces immersed into Riemannian space forms. Assuming an Okumura type inequality on the total umbilicity tensor of such hypersurfaces, we prove that either the hypersurface is totally umbilical or it holds an estimate for the norm of the total umbilicity tensor, which is also shown be sharp in the sense that the product of space forms realize them. Our approach is based on a version of the Omori–Yau maximum principle for a suitable Cheng–Yau type operator.
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- Research Article
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- © 2019 Australian Mathematical Publishing Association Inc.
Footnotes
The second author is partially supported by CNPq, Brazil, grant 303977/2015-9.
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