Geometric invariants and principal configurations on spacelike surfaces immersed in R^3,1

TL;DR

This paper explores geometric invariants and principal curvature configurations on spacelike surfaces in four-dimensional Minkowski space, focusing on lightlike normal fields and their influence on curvature line arrangements.

Contribution

It introduces numerical invariants related to the second fundamental form and analyzes principal curvature lines with lightlike normals on spacelike surfaces.

Findings

Characterization of invariants for spacelike surfaces in R^3,1

Analysis of lightcone principal curvature configurations

Observations on mean directionally curved and asymptotic lines

Abstract

We first describe the numerical invariants attached to the second fundamental form of a spacelike surface in four-dimensional Minkowski space. We then study the configuration of the nu-principal curvature lines on a spacelike surface, when the normal field nu is lightlike (the lightcone configuration). Some observations on the mean directionally curved lines and on the asymptotic lines on spacelike surfaces end the paper.