Transversal Intersection Curves of Two Surfaces in Minkowski 3-Space

• Alêssio, Osmar ^[2] ; Badr, Sayed A.-N. ^[3] ; Hassan, Soad A. ^[3] ; Rodrigues, Luciana A. ^[4] ; Silva, Fabio N. ^[5] ; Soliman, M.A. ^[1]
  1. [1] Assiut University

     Assiut University

     Egipto

     
  2. [2] Instituto de Cincias Exatas, Naturais e Educao - UFTM, Uberaba, MG, Brazil
  3. [3] Dept. of Math. Al-Qunfudah University College - Umm Al-Qura University, Al-Qunfudah, KSA
  4. [4] Departamento de Matematica - Universidade de Braslia , Brasilia, DF, Brazil
  5. [5] Centro das Ciencias Exatas e das Tecnologias - UFOB, Barreiras, BA, Brazil

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• Localización: Selecciones Matemáticas, ISSN-e 2411-1783, Vol. 5, Nº. 2 (Agosto - Diciembre), 2018, págs. 137-153
• Idioma: inglés
• DOI: 10.17268/sel.mat.2018.02.02
• Títulos paralelos:
  • Curvas dadas por la intersección transversal de dos superficies en el espacio tridimesional de Minkowski
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• Resumen
  • español

    En este artículo, estudiamos la geometría diferencial de la curva dada por la intersección transversal de dos superficies en el espacio tridimensional de Minkowski donde cada par satisface los siguientes tipos de superficies; tipo espacio - tipo luz, tipo tiempo - tipo luz y tipo luz - tipo luz. Generalmente, las superficies están dadas por sus ecuaciones paramétricas o implícitas, entonces el problema de intersección superficie superficie aparece comunmente como paramétrico-paramétrico, paramétrico-implícito e implícito-implícito. Obtenemos el Referencial de Frenet, el Referencial de Darboux, la curvatura, la torsión, la curvatura normal y las curvaturas geodésicas de las intersecciones transversales para todos los tipos de problemas de intersección. Mostramos que la curva de intersección puede ser una curva similar a una curva tipo espacio (tipo tiempo, tipo luz o pseudo nula). Finalmente, mostramos nuestros métodos por varios ejemplos.

  • English

    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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