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Mannheim curves and their partner curves in Minkowski 3-space E13

Elsharkawy Ayman, Elshenhab Ahmed M.

Demonstratio Mathematica

2022

Vol. 55, nr 1

798--811

The modified orthogonal frame is an important tool to study analytic space curves whose curvatures have discrete zero points. In this article, by using the modified orthogonal frame, Mannheim curves and their partner curves are investigated in Minkowski 3-space. Some characterizations according to the curvatures and torsions of the curves are given. Finally, some relations under the conditions for Mannheim curves and their partner curves to be generalized helices are presented. All the possible cases for the partner curves to be spacelike and timelike are considered in the whole of the article.

Lightlike developables in minkowski 3-space

Chino S., Izumiya S.

Demonstratio Mathematica

2010

Vol. 43, nr 2

387-399

We say that a surface in Minkowski 3-space is a lightlike developable if all pseudo-normal vectors of the regular part of the surface are lightlike. The tangent surface of a lightlike curve is one of the lightlike developables. We give a generic classification of such surfaces. The all arguments in this paper are elementary. However, we discovered the H3 type singularity appears in generic for such a class of surfaces. Since the H3 type singularity usually appears in non-generic situation, this is a quite interesting phenomenon.