Classification of rotational surfaces with constant skew curvature in 3-space forms
Differential Geometry
2020-05-18 v1
Abstract
In this paper, we classify the rotational surfaces with constant skew curvature in -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.
Keywords
Cite
@article{arxiv.2005.07671,
title = {Classification of rotational surfaces with constant skew curvature in 3-space forms},
author = {Rafael López and Álvaro Pámpano},
journal= {arXiv preprint arXiv:2005.07671},
year = {2020}
}
Comments
To appear in Journal of Mathematical Analysis and Applications