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- Title
A sharp integral inequality for closed spacelike submanifolds immersed in the de Sitter space.
- Authors
de Lima, Henrique F.; dos Santos, Fábio R.; Rocha, Lucas S.
- Abstract
In this paper, we establish a sharp integral inequality for n-dimensional closed spacelike submanifolds with constant scalar curvature immersed with parallel normalized mean curvature vector field in the de Sitter space S p n + p of index p, and we use it to characterize totally umbilical round spheres S n (r) , with r > 1 , of S 1 n + 1 ↪ S p n + p . Our approach is based on a suitable lower estimate of the Cheng-Yau operator acting on the square norm of the traceless second fundamental form of such a spacelike submanifold.
- Publication
Archiv der Mathematik, 2021, Vol 116, Issue 6, p683
- ISSN
0003-889X
- Publication type
Article
- DOI
10.1007/s00013-021-01587-z