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ON THE UMBILICITY OF HYPERSURFACES IN THE HYPERBOLIC SPACE

  • C. P. AQUINO (a1), M. BATISTA (a2) and H. F. DE LIMA (a3)

Abstract

In this paper, we establish new characterization results concerning totally umbilical hypersurfaces of the hyperbolic space $\mathbb{H}^{n+1}$ , under suitable constraints on the behavior of the Lorentzian Gauss map of complete hypersurfaces having some constant higher order mean curvature. Furthermore, working with different warped product models for $\mathbb{H}^{n+1}$ and supposing that certain natural inequalities involving two consecutive higher order mean curvature functions are satisfied, we study the rigidity and the nonexistence of complete hypersurfaces immersed in $\mathbb{H}^{n+1}$ .

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The first author is partially supported by CNPq, Brazil, grant number 302738/2014-2. The second author is partially supported by CNPq, Brazil, grant number 456755/2014-4. The third author is partially supported by CNPq, Brazil, grant number 303977/2015-9.

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ON THE UMBILICITY OF HYPERSURFACES IN THE HYPERBOLIC SPACE

  • C. P. AQUINO (a1), M. BATISTA (a2) and H. F. DE LIMA (a3)

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