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 (O. Bonnet, Euler, Liouville) are found in this space. Finally, the examples of these surfaces are given.

Timelike Surface Couple with Bertrand Couple as Joint Geodesic Curves in Minkowski 3-Space

“…Furthermore, in [44], the singularities are classified by the osculating developable surface, in addition to giving a relation between both the osculating Darboux vector fields and normal vector fields of timelike surfaces along the curve using Legendrian dualities. Additionally, in the Lorentz-Minkowski 3-space, the relation between geodesic torsions, normal curvatures and geodesic curvatures for parameter curves that intersect at any angle in case of timelike surfaces are investigated [45]. However, to the best of our knowledge, no work has focused on constructing T LSC using a BC as a pair of geodesic curves in the Minkowski 3-space E 3 1 .…”