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

2021/11/07 by Victor H. Patty-Yujra, Yujra, Victor H. Patty
Mathematics · Physics and Astronomy · #53B25 #53C42 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2111.04252

openalex publication_date 2021/11/08 · openalex created_date 2021/11/22 · openalex updated_date 2026/07/28

Abstract

A canonical normal null direction on a spacelike surface in the four dimensional Minkowski space ℝ^3,1 is a parallel vector field Z on 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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