Spacelike surfaces in Minkowski 4-space with a canonical normal null direction

Victor H. Patty Yujra

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arXiv · 2111.04252

Spacelike surfaces in Minkowski 4-space with a canonical normal null direction

Victor H. Patty Yujra

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Abstract

A canonical normal null direction on a spacelike surface in the four dimensional Minkowski space $\mathbb{R}^{3,1}$ is a parallel vector field $Z$ on $\mathbb{R}^{3,1}$ such that the normal component of $Z$ on the surface is a lightlike vector field. We describe the geometric properties of a spacelike surface endowed with a canonical normal null direction and we obtain some characterizations of these surfaces. Moreover, using their Gauss map we study other properties of these surface: the associated ellipse of curvature and their asymptotic directions. Finally, we give two different ways to create these surfaces, one of them involves a nonlinear partial differential equation.

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Victor H. Patty Yujra. 2021-11-08. Spacelike surfaces in Minkowski 4-space with a canonical normal null direction. https://arxiv.org/abs/2111.04252

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