Geometric Interpretation of det(C^(3),C^(4),C^(5))=0 in E13
Differential Geometry
2014-11-05 v1
Abstract
In this paper, we investigate the tangent indicatrix of the curve C with constant curvature. Tangent indicatrix of the curve C is characterized with det(C^(3),C^(4),C^(5))=0 in Minkowski 3-space E13. Moreover, we study null slant helices using the determinant approach and give the following characterization: A curve C is a null slant helix in E13 if and only if det(C^(3),C^(4),C^(5))=0. Then similar results are obtained for non-null curves with the condition k=1.
Keywords
Cite
@article{arxiv.1411.1013,
title = {Geometric Interpretation of det(C^(3),C^(4),C^(5))=0 in E13},
author = {Seher Kaya and Ismail Gok and Yusuf Yayli},
journal= {arXiv preprint arXiv:1411.1013},
year = {2014}
}