• Corpus ID: 244478293

# Canonical Coordinates and Natural Equation for Lorentz Surfaces in \$\mathbb R^3_1\$

```@inproceedings{Kanchev2021CanonicalCA,
title={Canonical Coordinates and Natural Equation for Lorentz Surfaces in \\$\mathbb R^3\_1\\$},
author={Krasimir Kanchev and Ognian Kassabov and Velichka Milousheva},
year={2021}
}```
• Published 20 November 2021
• Mathematics
We consider Lorentz surfaces in \$\mathbb R^3_1\$ satisfying the condition \$H^2-K\neq 0\$, where \$K\$ and \$H\$ are the Gauss curvature and the mean curvature, respectively, and call them Lorentz surfaces of general type. For this class of surfaces we introduce special isotropic coordinates, which we call canonical, and show that the coefficient \$F\$ of the first fundamental form and the mean curvature \$H\$, expressed in terms of the canonical coordinates, satisfy a special integro-differential…