Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4613747 | Journal of Mathematical Analysis and Applications | 2017 | 11 Pages |
Abstract
We deal with complete submanifolds MnMn having constant positive scalar curvature and immersed with parallel normalized mean curvature vector field in a Riemannian space form Qcn+p of constant sectional curvature c∈{1,0,−1}c∈{1,0,−1}. In this setting, we show that such a submanifold MnMn must be either totally umbilical or isometric to a Clifford torus S1(1−r2)×Sn−1(r), when c=1c=1, a circular cylinder R×Sn−1(r)R×Sn−1(r), when c=0c=0, or a hyperbolic cylinder H1(−1+r2)×Sn−1(r), when c=−1c=−1. This characterization theorem corresponds to a natural improvement of previous ones due to Alías, García-Martínez and Rigoli [2], Cheng [4] and Guo and Li [6].
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jogli G. Araújo, Henrique F. de Lima, Fábio R. dos Santos, Marco Antonio L. Velásquez,