Weingarten Type Surfaces in ℍ2 × ℝ and 𝕊2 × ℝ

Abstract

AbstractIn this article, we study complete surfaces Σ, isometrically immersed in the product spaces ℍ2 × ℝ or 𝕊2 × ℝ having positive extrinsic curvature Ke . Let Ki denote the intrinsic curvature of Σ. Assume that the equation aKi + bKe = c holds for some real constants a ≠ 0,b >0, and c. The main result of this article states that when such a surface is a topological sphere, it is rotational.