Hits:

Indexed by:期刊论文

Date of Publication:2015-01-01

Journal:Vietnam Journal of Mathematics

Included Journals:Scopus

Volume:43

Issue:4

Page Number:705-723

ISSN No.:2305221X

Abstract:By Moving Frame Method, we firstly derive some Simons type equations for an n-dimensional submanifold Mn with parallel mean curvature vector field    in (Formula presented.) , where Mm(c) is an m-dimensional space form of constant sectional curvature c and obtain a lower bound of the squared norm of the covariant differential of the second fundamental form h of Mn. Then, we use these results to prove some gap theorems on |h|2 and |?|2=|h|2?n|  |2. ? 2015, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.