Surfaces Family With Common Null Asymptotic

2014/09/02 by Gülnur Şaffak Atalay, Gulnur Saffak Atalay, Atalay, Gulnur Saffak +3
Computer Science · Engineering · Mathematics · #53A04 #53B30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.DG #msc:53A04 #msc:53B30

paper · pdf · doi:10.48550/arxiv.1409.1153

10 pages and 5 figures

arxiv created 2014/09/02 · openalex publication_date 2014/09/02 · arxiv updated 2014/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyzed the problem of finding a surfaces family through an asymptotic curve with Cartan frame. We obtain the parametric representation for surfaces family whose members have the same as an asymptotic curve. By using the Cartan frame of the given null curve, we present the surface as a linear combination of this frame and analysed the necessary and sufficient condition for that curve to satisfy the asymptotic requirement. We illustrate the method by giving some examples.

Related

• Surfaces with a common asymptotic curve in Minkowski 3-space
• An approach for designing a surface pencil through a given asymptotic curve
• Surface family with a common natural asymptotic lift of a timelike curve in Minkowski 3-space
• Asymptotically Poincaré surfaces in quasi-Fuchsian manifolds
• A view-parametric extension of the d'Ocagne formula for a surface in ℝ³