Classification of rotational surfaces with constant skew curvature in 3-space forms

Abstract

In this paper, we classify the rotational surfaces with constant skew curvature in 3-space forms. We also give a variational characterization of the profile curves of these surfaces as critical points of a curvature energy involving the exponential of the curvature of the curve. Finally, we provide a converse process to produce all rotational surfaces with constant skew curvature based on the evolution of a critical curve under the flow of its binormal vector field with prescribed velocity.