Nontrivial minimal surfaces in a class of Finsler 3-spheres

Abstract

In this paper, we study the rotationally invariant minimal surfaces in the Bao–Shen's spheres, which are a class of 3-spheres endowed with Randers metrics [Formula: see text] of constant flag curvature K = 1, where [Formula: see text] are Berger metrics, [Formula: see text] are one-forms and k > 1 is an arbitrary real number. We obtain a class of nontrivial minimal surfaces isometrically immersed in the Bao–Shen's spheres, which is the first class of nontrivial minimal surfaces with respect to the Busemann–Hausdorff measure in Finsler spheres. Moreover, we also obtain a new class of explicit minimal surfaces in the classical Berger spheres [Formula: see text], which was expected to get in [F. Torralbo, Rotationally invariant constant mean curvature surfaces in homogeneous 3-manifolds, Differential Geom. Appl.28(5) (2010) 593–607].