Asymptotic and Geodesic Bishop Curves in Three Dimensions Minkowski Space E_1^3

Biharmonic Curves in Minkowski 3-space

We give a differential geometric interpretation for the classification of biharmonic curves in semi-Euclidean 3-space due to Chen and Ishikawa (1991).

Planar Cubic Space-like Bézier Curves in Three Dimensional Minkowski Space

This paper considers planar cubic Bézier curves in three-dimensional Minkowski space. We shall consider the conditions for the control points A,C,D,B of the Bézier curve such that the Bézier segment is pointwise space-like. For the control point C, we shall give a geometrical interpretation of the feasibility condition provided the rest of the control points are fixed.

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.

Pseudoholomorphic Curves and Dynamics in Three Dimensions

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.