Some Characterizations of Translation Surface Generated by Spherical Indicatrices of Timelike Curves in Minkowski 3-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.

Generalized Timelike Mannheim Curves in Minkowski Space - Time E 41

Weierstrass Representation for Timelike Minimal Surfaces in Minkowski 3-space

Using techniques of integrable systems, we study a Weierstraß representation formula for timelike surfaces with prescribed mean curvature in Minkowski 3-space. It is shown that timelike minimal surfaces are obtained by integrating a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in Minkowski 3-space. The relationship between timelike minimal surfaces and bosonic Nambu-Goto ...

New special curves and their spherical indicatrices

From the view of differential geometry, a straight line is a geometric curve with the curvature κ(s) = 0. A plane curve is a family of geometric curves with torsion τ(s) = 0. Helix is a geometric curve with non-vanishing constant curvature κ and non-vanishing constant torsion τ [4]. The helix may be called a circular helix or W -curve [9]. It is known that straight line (κ(s) = 0) and circle (κ...

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).