Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature

Details Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature

2010-06-11

arxiv.org/abs/1006.2345v2

Mathematics

Differential Geometry

19 pages, 1 figure

Scientific paper

In this work we find all helicoidal surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is $0$ or $1$ and that the surface is ruled. If the generating curve is a Lorentzian circle, we show that the only possibility is that the axis is spacelike and the center of the circle lies in the axis.

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