Abstract
We provide sharp lower and upper bounds for the supremum of the norm of the total umbilicity tensor of complete spacelike hypersurfaces with constant scalar curvature immersed in a Lorentzian space form and satisfying a suitable Okumura-type inequality, which corresponds to a weaker hypothesis when compared with the geometric condition of the hypersurface having two distinct principal curvatures. Furthermore, we give a complete description and the gaps of the spacelike hypersurfaces which realize our estimates, obtaining as a consequence new characterizations of totally umbilical spacelike hypersurfaces and hyperbolic cylinders of Lorentzian space forms. Our approach is based on a version of Omori–Yau’s maximum principle for trace-type differential operators defined on a complete Riemannian manifold.
Citation
A. Gervasio Colares. Eudes L. de Lima. Henrique F. de Lima. "Complete spacelike hypersurfaces with constant scalar curvature: Descriptions and gaps." Illinois J. Math. 65 (4) 769 - 792, December 2021. https://doi.org/10.1215/00192082-9619615
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