Complete CSC Hypersurfaces Satisfying an Okumura-Type Inequality in Ricci Symmetric Manifolds
Keyword(s):
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.
2001 ◽
Vol 73
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pp. 327-332
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2001 ◽
Vol 64
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pp. 755-768
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2006 ◽
Vol 73
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pp. 9-16
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pp. 287-296
2019 ◽
Vol 16
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pp. 1950039
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Vol 137
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pp. 2293-2298
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Vol 55
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pp. 474-486
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