English

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 33-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