## Kodai Mathematical Journal

### Linear Weingarten submanifolds immersed in a space form

#### 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].

#### Article information

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

Dates
First available in Project Euclid: 12 July 2017

https://projecteuclid.org/euclid.kmj/1499846595

Digital Object Identifier
doi:10.2996/kmj/1499846595

Mathematical Reviews number (MathSciNet)
MR3680559

Zentralblatt MATH identifier
1372.53060

#### Citation

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