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 K=−1, which are the first examples of BH‐minimal surfaces in the hyperbolic Randers space.

On Minimal Surfaces Immersed in Three Dimensional Kropina Minkowski Space

“…Further Souza et al obtained a Bernstein type theorem for minimal surfaces in a Randers space [22]. Minimal surfaces in a Randers space have been studied by several authors [8][9][10]18]. Recently, minimal surface with Matsumoto metric has been studied in [11].…”

On Minimal Surfaces of Revolutions Immersed in Deformed Hyperbolic Kropina Space

“…al., have studied the minimal surfaces of revolution and the surfaces defined by the graphs of functions in Minkowski space R 3 with Randers metric; and have obtained some interesting results [19,20]. Minimal surfaces in various Randers spaces have been thoroughly investigated by Geometers, see e.g., [7,8,9,10]. A class of minimal surfaces with Matsumoto metrics and Kropina metrics have been recently investigated in [12] and [13] respectively.…”

On minimal surfaces immersed in three dimensional Kropina Minkowski space

“…Further Souza et al obtained a Bernstein type theorem for minimal surfaces in a Randers space [22]. Minimal surfaces in a Randers space have been studied by several authors [8,9,10,18]. Recently, minimal surface with Matsumoto metric has been studied in [11].…”