Remarks on minimal surfaces in a 3-dimensional Randers space

Abstract

In this paper, we study minimal surfaces in Randers space. We consider Randers metric $$F=\alpha +\beta $$ , on the 3-dimensional real vector space V, where $$\alpha $$ is the Euclidean metric, and $$\beta $$ is a 1-form with norm b satisfying $$0\le b<1$$ . We firstly solve the ordinary differential equation that characterizes the rotational minimal surfaces in (V, F) and discuss the geometrical properties of the meridian curves. Then we obtain the ordinary differential equation that characterizing the minimal translation surface in (V, F). Finally we prove that the only minimal surfaces in (V, F) are plane.