Spacelike surfaces in Minkowski space satisfying a linear relation between their principal curvatures

2010/03/23 by Özgür KALKAN, Kalkan, Özgür Boyacıoğlu, Rafael López +1 · 1 citation
Mathematics · Physics and Astronomy · #53A10 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1003.4550

openalex publication_date 2010/03/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this work, we consider spacelike surfaces in Minkowski space \hbox\bf E%₁³ that satisfy a linear Weingarten condition of type κ₁=mκ₂+n, where m and n are constant and κ₁ and κ₂ denote the principal curvatures at each point of the surface. We study the family of surfaces foliated by a uniparametric family of circles in parallel planes. We prove that the surface must be rotational or the surface is part of the family of Riemann examples of maximal surfaces (m=-1, n=0). Finally, we consider the class of rotational surfaces for the case n=0, obtaining a first integration if the axis is timelike and spacelike and a complete description if the axis is lightlike.

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• Rotational Weingarten surfaces in Lorentz-Minkowski space

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