Weingarten type surfaces in ℍ²×ℝ and \mathbbS²×ℝ

2015/11/25 by Folha, Abigail, Peñafiel, Carlos
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1511.08146

Abstract

In this article, we study complete surfaces Σ, isometrically immersed in the product space ℍ²×ℝ or \mathbbS²×ℝ having positive extrinsic curvature K_e. Let K_i denote the intrinsic curvature of Σ. Assume that the equation aK_i+bK_e=c holds for some real constants a≠0, b>0 and c. The main result of this article state that when such a surface is a topological sphere it is rotational.

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