# Transversal Intersection Curves of Two Surfaces in Minkowski 3-Space

## Authors

• Osmar Alêssio Instituto de Ciencias Exatas, Naturais e Educao - UFTM, Uberaba, MG, Brazil
• Sayed A.-N. Badr Dept. of Math. Al-Qunfudah University College - Umm Al-Qura University, Al-Qunfudah, KSA
• Soad A. Hassan Dept. of Math. Al-Qunfudah University College - Umm Al-Qura University, Al-Qunfudah, KSA
• Luciana A. Rodrigues Departamento de Matemática - Universidade de Braslia , Brasilia, DF, Brazil
• Fabio N. Silva Centro das Ciencias Exatas e das Tecnologias - UFOB, Barreiras, BA, Brazil
• M.A. Soliman Dept. of Math.- Faculty of Science - Assiut University, Assiut, Egypt

## Keywords:

Minkowski 3-Space, Surface-Surface intersection, Pseudo null curve, Null curve, Null frame, Lightlike surface, Darboux Frame

## Abstract

In this paper, we study the differential geometry of the transversal intersection curve of two surfaces in Minkowski 3-space, where each pair satisfies the following types spacelike-lightlike, timelike-lightlike and lightlike-lightlike. Surfaces are generally give by their parametric or implicit equations, then the surfacesurface intersection problem appear commonly as parametric-parametric, parametric-implicit and implicitimplicit.
We derive the Frenet frame, Darboux frame, curvature, torsion, normal curvature and geodesic curvatures of transversal intersections for all types of intersection problems. We show the intersection curve may be spacelike (timelike, lightlike or pseudo null) curve. Finally, we show our methods by given several examples.

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2018-12-30

## How to Cite

Alêssio, O., Badr, S. A.-N., Hassan, S. A., Rodrigues, L. A., Silva, F. N., & Soliman, M. (2018). Transversal Intersection Curves of Two Surfaces in Minkowski 3-Space. Selecciones Matemáticas, 5(02), 137-153. https://doi.org/10.17268/sel.mat.2018.02.02

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