Complete CSC Hypersurfaces Satisfying an Okumura-Type Inequality in Ricci Symmetric Manifolds

Mathematics

卷:9

Chao Yang¹  Xun Xie¹  Jiancheng Liu¹ 

[1] School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China;

关键词: Ricci symmetric manifolds;    Einstein manifolds;    Okumura-type inequality;    constant scalar curvature;    spacelike hypersurface;   

DOI  :  10.3390/math9222914

来源: DOAJ

【 摘 要 】

We investigate the spacelike hypersurface with constant scalar curvature (SCS) immersed in a Ricci symmetric manifold obeying standard curvature constraints. By supposing these hypersurfaces satisfy a suitable Okumura-type inequality recently introduced by Meléndez, which is a weaker hypothesis than to assume that they have two distinct principal curvatures, we obtain a series of umbilicity and pinching results. In particular, when the Ricci symmetric manifold is an Einstein manifold, then we further obtain some rigidity classifications of such hypersufaces.

【 授权许可】

Unknown