Differential Geometry of Curves and Surfaces in Lorentz-Minkowski space

TL;DR

This paper reviews classical differential geometry of curves and surfaces in Lorentz-Minkowski space, emphasizing spacelike surfaces with constant mean curvature and comparing them to Euclidean space counterparts.

Contribution

It provides a focused review on spacelike surfaces with constant mean curvature in Lorentz-Minkowski space, highlighting differences and similarities with Euclidean geometry.

Findings

Characterization of spacelike surfaces with constant mean curvature.

Comparison between Lorentz-Minkowski and Euclidean geometries.

Insights into the classical theory adapted to Lorentzian setting.

Abstract

We review part of the classical theory of curves and surfaces in $3$-dimensional Lorentz-Minkowski space. We focus in spacelike surfaces with constant mean curvature pointing the differences and similarities with the Euclidean space.