Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024554 | Nonlinear Analysis: Theory, Methods & Applications | 2017 | 13 Pages |
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 Qcn+p of constant sectional curvature c and with nâ¥4. We recall that a submanifold is called linear Weingarten when its mean and scalar curvatures are linearly related. In this setting, we establish a suitable extension of the generalized maximum principle of Omori-Yau in order to show that such a submanifold Mn must be either totally umbilical or isometric to a Clifford torus S1(1âr2)ÃSnâ1(r), when c=1, a circular cylinder RÃSnâ1(r), when c=0, or a hyperbolic cylinder H1(â1+r2)ÃSnâ1(r), when c=â1. We also study the parabolicity of these submanifolds with respect to a Cheng-Yau modified operator.
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Authors
Henrique F. de Lima, Fábio R. dos Santos,