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...
| Autori principali: | , , |
|---|---|
| Natura: | Articolo |
| Lingua: | English |
| Pubblicazione: |
MDPI AG
2021-11-01
|
| Serie: | Mathematics |
| Soggetti: | |
| Accesso online: | https://www.mdpi.com/2227-7390/9/22/2914 |
| Riassunto: | 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. |
|---|---|
| ISSN: | 2227-7390 |