On minimal surfaces in a class of Finsler 3-spheres (Q2439337)

The present paper is devoted to minimal surfaces in a Bao-Shen sphere which is \(S^3\) with a Randers metric associated to a Killing vector field tangent to the Hopf fibers. More precisely, for \(c\in \mathbb{R}\) it is proved that the helicoids \(f_c:\mathbb{R}^2\rightarrow S^3\) given by \(f_c(s, t)=(\cos s\, e^{ict}, \sin s\, e^{it})\) are minimal with respect to the Busemann-Hausdorff volume form. Also, some rigidity results are obtained.