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

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...

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Main Authors:	Xun Xie, Jiancheng Liu, Chao Yang
Format:	article
Language:	EN
Published:	MDPI AG 2021
Subjects:	Ricci symmetric manifolds Einstein manifolds Okumura-type inequality constant scalar curvature spacelike hypersurface Mathematics QA1-939
Online Access:	https://doaj.org/article/4256c5381b724f0c87b05ed94e91c224
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spelling	oai:doaj.org-article:4256c5381b724f0c87b05ed94e91c2242021-11-25T18:17:10ZComplete CSC Hypersurfaces Satisfying an Okumura-Type Inequality in Ricci Symmetric Manifolds10.3390/math92229142227-7390https://doaj.org/article/4256c5381b724f0c87b05ed94e91c2242021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2914https://doaj.org/toc/2227-7390We 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.Xun XieJiancheng LiuChao YangMDPI AGarticleRicci symmetric manifoldsEinstein manifoldsOkumura-type inequalityconstant scalar curvaturespacelike hypersurfaceMathematicsQA1-939ENMathematics, Vol 9, Iss 2914, p 2914 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Ricci symmetric manifolds Einstein manifolds Okumura-type inequality constant scalar curvature spacelike hypersurface Mathematics QA1-939
spellingShingle	Ricci symmetric manifolds Einstein manifolds Okumura-type inequality constant scalar curvature spacelike hypersurface Mathematics QA1-939 Xun Xie Jiancheng Liu Chao Yang Complete CSC Hypersurfaces Satisfying an Okumura-Type Inequality in Ricci Symmetric Manifolds
description	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.
format	article
author	Xun Xie Jiancheng Liu Chao Yang
author_facet	Xun Xie Jiancheng Liu Chao Yang
author_sort	Xun Xie
title	Complete CSC Hypersurfaces Satisfying an Okumura-Type Inequality in Ricci Symmetric Manifolds
title_short	Complete CSC Hypersurfaces Satisfying an Okumura-Type Inequality in Ricci Symmetric Manifolds
title_full	Complete CSC Hypersurfaces Satisfying an Okumura-Type Inequality in Ricci Symmetric Manifolds
title_fullStr	Complete CSC Hypersurfaces Satisfying an Okumura-Type Inequality in Ricci Symmetric Manifolds
title_full_unstemmed	Complete CSC Hypersurfaces Satisfying an Okumura-Type Inequality in Ricci Symmetric Manifolds
title_sort	complete csc hypersurfaces satisfying an okumura-type inequality in ricci symmetric manifolds
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/4256c5381b724f0c87b05ed94e91c224
work_keys_str_mv	AT xunxie completecschypersurfacessatisfyinganokumuratypeinequalityinriccisymmetricmanifolds AT jianchengliu completecschypersurfacessatisfyinganokumuratypeinequalityinriccisymmetricmanifolds AT chaoyang completecschypersurfacessatisfyinganokumuratypeinequalityinriccisymmetricmanifolds
_version_	1718411375284322304

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

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