Helicoidal Minimal Surfaces in a Finsler Space of Randers Type

Abstract

AbstractWe consider the Finsler spaceobtained by perturbing the Euclidean metric of ℝ3by a rotation. It is the open region of ℝ3 bounded by a cylinder with a Randers metric. Using the Busemann–Hausdorff volume form, we obtain the differential equation that characterizes the helicoidal minimal surfaces in. We prove that the helicoid is a minimal surface inonly if the axis of the helicoid is the axis of the cylinder. Moreover, we prove that, in the Randers space, the only minimal surfaces in the Bonnet family with fixed axis Ox̄3are the catenoids and the helicoids.