Linear Weingarten submanifolds immersed in a space form

Abstract

In this paper, we deal with complete linear Weingarten submanifolds Mⁿ immersed with parallel normalized mean curvature vector field in a Riemannian space form 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 Mⁿ 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].