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

zbMATH Open1247.53018arXiv1003.4550MaRDI QIDQ2901316

Rafael López, Özgür Boyacioglu Kalkan

Publication date: 19 July 2012

Abstract: In this work, we consider spacelike surfaces in Minkowski space $$ that satisfy a linear Weingarten condition of type $kapp{a}_1=mkapp{a}_2+n$, where $m$ and $n$ are constant and $kapp{a}_1$ and $kapp{a}_2$ 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.

Full work available at URL: https://arxiv.org/abs/1003.4550

zbMATH Keywords

Minkowski spacespace-likeprincipal curvaturesWeingarten surfaces

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Local submanifolds (53B25) Non-Euclidean differential geometry (53A35)

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