Surfaces of revolution with constant mean curvature in Lorentz-Minkowski space
In a classical paper [Sur la surface de révolution dont la courbure moyenne est constante, J. Math. Pures Appl. 6, 309-320 (1841)] \textit{Ch. Delaunay} proved that the profile curve of a surface of revolution with nonzero constant mean curvature in Euclidean 3-space can be described as the locus of a focus, when a quadratic curve is rolled along the axis of revolution. In the present paper we study the problem in Lorentz- Minkowski 3-space by considering spacelike surfaces of revolution. In the case where the axis of revolution is spacelike or timelike we obtain results similar to Delaunay's except that the nature of quadrics needs special attention. In the case where the axis is a null line we can determine the profile curves completely without giving a geometric interpretation.
scientific article; zbMATH DE number 3849994