CMC biconservative surfaces in ${\mathbb{S}}^n\times \mathbb{R}$ and ${\mathbb{H}}^n\times \mathbb{R}$

Abstract

We classify non-minimal biconservative surfaces with parallel mean curvature vector field in ${\mathbb{S}}^n\times \mathbb{R}$ and ${\mathbb{H}}^n\times \mathbb{R}$. When these surfaces do not lie in ${\mathbb{S}}^n$ or ${\mathbb{H}}^n$ 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.

19 pages

Cited by in corpus (1)

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