CMC biconservative surfaces in \mathbbSⁿ×ℝ and ℍⁿ×ℝ

2014/08/22 by Fetcu, Dorel, Oniciuc, Cezar, Pinheiro, Ana Lucia
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1408.5437

Abstract

We classify non-minimal biconservative surfaces with parallel mean curvature vector field in \mathbbSⁿ×ℝ and ℍⁿ×ℝ. When these surfaces do not lie in \mathbbSⁿ or ℍⁿ and they are not vertical cylinders, we find their explicit (local) equation. We also prove a result on the compactness of biconservative surfaces with constant mean curvature in Hadamard manifolds.

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