# RIGIDITY THEOREMS IN THE HYPERBOLIC SPACE

• De Lima, Henrique Fernandes (Departamento de Matematica e Estatistica Universidade Federal de Campina Grande)
• Published : 2013.01.31
• 105 9

#### Abstract

As a suitable application of the well known generalized maximum principle of Omori-Yau, we obtain rigidity results concerning to a complete hypersurface immersed with bounded mean curvature in the $(n+1)$-dimensional hyperbolic space $\mathbb{H}^{n+1}$. In our approach, we explore the existence of a natural duality between $\mathbb{H}^{n+1}$ and the half $\mathcal{H}^{n+1}$ of the de Sitter space $\mathbb{S}_1^{n+1}$, which models the so-called steady state space.

#### Keywords

hyperbolic space;complete hypersurfaces;mean curvature;Gauss map

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#### Cited by

1. On Bernstein-Type Theorems in Semi-Riemannian Warped Products vol.2013, 2013, https://doi.org/10.1155/2013/959143