Minimal surfaces in a Randers sphere with the rotational Killing vector field

The minimal surfaces in Finsler geometry with respect to the Busemann–Hausdorff measure and the Holmes–Thompson measure are called BH-minimal and HT-minimal surfaces, respectively. Let (p1,p2,p3,p4)(p1,p2,p3,p4) be the coordinates of R4R4 and (S3,F˜) be a Randers sphere of flag curvature K=1K=1 with the navigation data (h˜,W˜), where h˜ is the standard sphere metric and W˜=ε(0,0,−p4,p3), 0<ε<10<ε<1, is a Killing vector field. In this paper, we study the rotationally invariant minimal surface in (S3,F˜) generated by rotating the curve (x(s),y(s),z(s),0)(x(s),y(s),z(s),0) in the upper half sphere of S2S2 around the p1p2p1p2-plane, s∈Rs∈R. We first show that such a rotational BH-minimal surface in (S3,F˜) is either a great 2-sphere or the catenoid in (S3,h˜). Then we give a classification of the rotational HT-minimal surfaces, where we use the angle data to analyze the solutions of the system of ODE that characterizes the HT-minimality and prove that, such a rotational HT-minimal surface must be a great 2-sphere, an HT-minimal torus, or a rotational surface of unduloid type. As a special case, we obtain a distinguished embedded compact HT-minimal torus depending on ε. The completeness of these surfaces is also studied.