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arXiv · 1708.06998

Timelike surfaces in Minkowski space with a canonical null direction

Victor H. Patty-Yujra·Gabriel Ruiz-Hernández
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Abstract

Given a constant vector field $Z$ in Minkowski space, a timelike surface is said to have a canonical null direction with respect to $Z$ if the projection of $Z$ on the tangent space of the surface gives a lightlike vector field. In this paper we describe these surfaces in the ruled case. For example when the Minkowski space has three dimensions then a surface with a canonical null direction is minimal and flat. On the other hand, we describe several properties in the non ruled case and we partially describe these surfaces in four-dimensional Minkowski space. We give different ways for building these surfaces in four-dimensional Minkowski space and we finally use the Gauss map for describe another properties of these surfaces.

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Victor H. Patty-Yujra, Gabriel Ruiz-Hernández. 2017-08-23. Timelike surfaces in Minkowski space with a canonical null direction. https://arxiv.org/abs/1708.06998

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