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

Abstract

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

14 pages, 1 figure

References in corpus (1)

• Sphere-foliated minimal and constant mean curvature hypersurfaces in product spaces

Cited by in corpus (1)

• Note on Surfaces of Revolution with an Affine-Linear Relation between their Curvature Radii