Generalized Spacelike Normal Curves in Minkowski Three-Space

Spacelike and Timelike Normal Curves in Minkowski Space-time

We define normal curves in Minkowski space-time E4 1 . In particular, we characterize the spacelike normal curves in E4 1 whose Frenet frame contains only non-null vector fields, as well as the timelike normal curves in E4 1 , in terms of their curvature functions. Moreover, we obtain an explicit equation of such normal curves with constant curvatures.

Spacelike Salkowski and anti-Salkowski Curves With a Spacelike Principal Normal in Minkowski 3-Space

A century ago, Salkowski [9] introduced a family of curves with constant curvature but non-constant torsion (Salkowski curves) and a family of curves with constant torsion but nonconstant curvature (anti-Salkowski curves). In this paper, we adapt definition of such curves to spacelike curves in Minkowski 3-space. Thereafter, we introduce an explicit parametrization of a spacelike Salkowski curv...

Caustics of de Sitter spacelike curves in Minkowski 3-space

In this paper, we consider evolutes of spacelike curves in de Sitter 2-space. Applying the theory of singularity theory, we find that these evolutes can be seen as one dimensional caustics which are locally diffeomorphic to lines or ordinary cusps. We establish the relationships between singularities of caustics and geometric invariants of curves under the action of the Lorentz group. c ©2016 A...

Pseudo-spherical evolutes of curves on a spacelike surface in three dimensional Lorentz-Minkowski space

In this paper we introduce the notion of pseudo-spherical evolutes of curves on a spacelike surface in three dimensional Lorentz-Minkowski space which is analogous to the notion of evolutes of curves on the hyperbolic plane. We investigate the the singularities and geometric properties of pseudo-spherical evolutes of curves on a spacelike surface.

Generalized Timelike Mannheim Curves in Minkowski Space - Time E 41