Helicoidal surfaces in three-dimensional Minkowski space

Abstract

In this paper we solve the problem of finding explicitly the helicoidal surfaces of the Minkowski space R 1 3 with prescribed Gaussian or mean curvature given by smooth functions. We distinguish three kinds of helicoidal surfaces corresponding to the space-like, time-like or light-like axes of revolution and give some geometric meanings of the helicoidal surfaces of the space-like type. We also define certain solinoid (tubular) surfaces of type I − around a hyperbolic helix in R 1 3 and study some of their geometric properties.