Nontrivial minimal surfaces in a hyperbolic Randers space

Abstract

The contribution of this paper is two‐fold. The first one is to derive a simple formula of the mean curvature form for a hypersurface in the Randers space with a Killing vector field, by considering the Busemann–Hausdorff measure and Holmes–Thompson measure simultaneously. The second one is to obtain the explicit local expressions of two types of nontrivial rotational BH‐minimal surfaces in a Randers domain of constant flag curvature , which are the first examples of BH‐minimal surfaces in the hyperbolic Randers space.