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

Xun Xie, Jiancheng Liu and Chao Yang
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Xun Xie: School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
Jiancheng Liu: School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
Chao Yang: School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Mathematics, 2021, vol. 9, issue 22, 1-15

Abstract: 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.

Keywords: Ricci symmetric manifolds; Einstein manifolds; Okumura-type inequality; constant scalar curvature; spacelike hypersurface (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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