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December 2021 Complete spacelike hypersurfaces with constant scalar curvature: Descriptions and gaps
A. Gervasio Colares, Eudes L. de Lima, Henrique F. de Lima
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Illinois J. Math. 65(4): 769-792 (December 2021). DOI: 10.1215/00192082-9619615

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.

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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

Information

Received: 20 October 2020; Revised: 25 October 2021; Published: December 2021
First available in Project Euclid: 2 December 2021

Digital Object Identifier: 10.1215/00192082-9619615

Subjects:
Primary: 53C42
Secondary: 53C50

Rights: Copyright © 2021 by the University of Illinois at Urbana–Champaign

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Vol.65 • No. 4 • December 2021
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