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

Rafael López; Álvaro Pámpano

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arXiv · 2005.07671

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

Rafael López·Álvaro Pámpano

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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.

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Rafael López, Álvaro Pámpano. 2020-05-15. Classification of rotational surfaces with constant skew curvature in 3-space forms. https://arxiv.org/abs/2005.07671

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