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 md5=24c0aadbae874e4aaa7973721c8db4df" 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 md5=17f2021af5c738feb1e24d284b6d523b"> of constant sectional curvature md5=d8f836e263482921d78edb75196251cd" title="Click to view the MathML source">c∈{1,0,−1}. In this setting, we show that such a submanifold md5=24c0aadbae874e4aaa7973721c8db4df" title="Click to view the MathML source">Mn must be either totally umbilical or isometric to a Clifford torus md5=45e952c267031d5ba0bff52826c2248f">, when md5=7093a35163339d2a3eae580756d9358f" title="Click to view the MathML source">c=1, a circular cylinder md5=edf33505c16a6f0a6158e02a080b0d6d" title="Click to view the MathML source">R×Sn−1(r), when md5=1a68b6514c1848b466bd38deb8850255" title="Click to view the MathML source">c=0, or a hyperbolic cylinder md5=dba62e31d95b3c62b6ddfd5666a28383">, when md5=4c8f5d7421a3442df706f82f06362a7e" title="Click to view the MathML source">c=−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].