The Darboux Trihedrons of Regular Curves on a Regular Time-Like Surface

Emin Özyilmaz

doi:10.3390/mca19020172

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Article

1 August 2014

The Darboux Trihedrons of Regular Curves on a Regular Time-Like Surface

Department of Mathematics, Faculty of Science, Ege University, TR-35100 İzmir, Turkey

Math. Comput. Appl.2014, 19(2), 172-183;https://doi.org/10.3390/mca19020172

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Abstract

In this work, we study Differential Geometry in the Minkowski 3-space R₁³ of the curves on a time-like regular surface by using parameter curves which are not perpendicular to each other. The aim of this study is to investigate the formulae between the Darboux Vectors of the time-like curve (c) , the time-like parameter curve (c₁) and the space-like parameter curve (c₂) which are not intersecting perpendicularly.

Keywords:

time-like and space-like curves; time-like surface; minkowski 3-space

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