Geometric Properties of Timelike Surfaces in Lorentz-Minkowski 3-Space

Abstract

In this paper, the relationships between geodesic torsions, normal curvatures and geodesic curvatures of the parameter curves intersecting at any angle on timelike surfaces in Lorentz-Minkowski 3-space are obtained by various equations. In addition, new equivalents of well-known formulas such as O. Bonnet, Euler, Liouville, Enneper are found in this space. Moreover, the different expressions of Gaussian curvature, which is one of the invariants of a timelike surface, are calculated. Finally, the examples of these surfaces are given.