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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Xun Xie & Jiancheng Liu & Chao Yang, 2021. "Complete CSC Hypersurfaces Satisfying an Okumura-Type Inequality in Ricci Symmetric Manifolds," Mathematics, MDPI, vol. 9(22), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2914-:d:679991
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