Kodai Mathematical Journal

Linear Weingarten submanifolds immersed in a space form

Henrique Fernandes De Lima, Fábio Reis Dos Santos, Jogli Gidel Da Silva Araújo, and Marco Antonio Lázaro Velásquez

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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].

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Kodai Math. J., Volume 40, Number 2 (2017), 214-228.

First available in Project Euclid: 12 July 2017

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De Lima, Henrique Fernandes; Dos Santos, Fábio Reis; Da Silva Araújo, Jogli Gidel; Velásquez, Marco Antonio Lázaro. Linear Weingarten submanifolds immersed in a space form. Kodai Math. J. 40 (2017), no. 2, 214--228. doi:10.2996/kmj/1499846595. https://projecteuclid.org/euclid.kmj/1499846595

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