刊名:Journal of Mathematical Analysis and Applications
出版年:2017
出版时间:1 March 2017
年:2017
卷:447
期:1
页码:488-498
全文大小:313 K
文摘
We deal with complete submanifolds bae874e4aaa7973721c8db4df" title="Click to view the MathML source">Mn having constant positive scalar curvature and immersed with parallel normalized mean curvature vector field in a Riemannian space form of constant sectional curvature c∈{1,0,−1}. In this setting, we show that such a submanifold bae874e4aaa7973721c8db4df" title="Click to view the MathML source">Mn must be either totally umbilical or isometric to a Clifford torus ba0bff52826c2248f">, when ae580756d9358f" title="Click to view the MathML source">c=1, a circular cylinder R×Sn−1(r), when c=0, or a hyperbolic cylinder ba62e31d95b3c62b6ddfd5666a28383">, when c=−1. This characterization theorem corresponds to a natural improvement of previous ones due to Alías, García-Martínez and Rigoli bbr0020">[2], Cheng bbr0040">[4] and Guo and Li bbr0060">[6].