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

2020/05/15 by Rafael López, López, Rafael, Álvaro Pámpano +1
Mathematics · Physics and Astronomy · #34C05 #37K25 #53A10 #53C42 #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2005.07671

openalex publication_date 2020/05/15 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Quantum mechanics with constraints

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