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June 2017 Linear Weingarten submanifolds immersed in a space form
Henrique Fernandes De Lima, Fábio Reis Dos Santos, Jogli Gidel Da Silva Araújo, Marco Antonio Lázaro Velásquez
Kodai Math. J. 40(2): 214-228 (June 2017). DOI: 10.2996/kmj/1499846595

Abstract

In this paper, we deal with complete linear Weingarten submanifolds $M^n$ immersed with parallel normalized mean curvature vector field in a Riemannian space form $\mathbf{Q}_c^{n+p}$ of constant sectional curvature $c$. Under an appropriated restriction on the norm of the traceless part of the second fundamental form, we show that such a submanifold $M^n$ must be either totally umbilical or isometric to a Clifford torus, if $c = 1$, a circular cylinder, if $c = 0$, or a hyperbolic cylinder, if $c = −1$. We point out that our results are natural generalizations of those ones obtained in [2] and [6].

Citation

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Henrique Fernandes De Lima. Fábio Reis Dos Santos. Jogli Gidel Da Silva Araújo. Marco Antonio Lázaro Velásquez. "Linear Weingarten submanifolds immersed in a space form." Kodai Math. J. 40 (2) 214 - 228, June 2017. https://doi.org/10.2996/kmj/1499846595

Information

Published: June 2017
First available in Project Euclid: 12 July 2017

zbMATH: 1372.53060
MathSciNet: MR3680559
Digital Object Identifier: 10.2996/kmj/1499846595

Rights: Copyright © 2017 Tokyo Institute of Technology, Department of Mathematics

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Vol.40 • No. 2 • June 2017
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