DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IN LORENTZ-MINKOWSKI SPACE

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. Contents 1. The Lorentz-Minkowski space E 3 1 45 2. Curves in Minkowski space 53 3. Surfaces in Minkowski space 72 4. Spacelike surfaces with constant mean curvature 91 5. Elliptic equations on cmc spacelike surfaces 99 References 106