# Hyperbolic surfaces of $L_1$-2-type

Document Type: Research Paper

Authors

1 Departamento de Matemáticas‎, ‎Facultad de Matemáticas‎, ‎Universidad de Murcia‎, ‎30100 Murcia‎, ‎Spain.

2 Departamento de Matemáticas‎, ‎Facultad de Ciencias‎, ‎Universidad Nacional de Colombia‎, ‎Bogotá DC‎, ‎Colombia.

Abstract

In this paper, we show that an $L_1$-2-type surface in the three-dimensional hyperbolic space $H^3\subset R^4_1$ either is an open piece of a standard Riemannian product $H^1(-\sqrt{1+r^2})\times S^{1}(r)$, or it has non constant mean curvature, non constant Gaussian curvature, and non constant principal curvatures.

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### History

• Receive Date: 31 July 2016
• Revise Date: 11 October 2016
• Accept Date: 14 October 2016