Construction of surface pencil with a given spacelike adjoint curve
Advanced Studies: Euro-Tbilisi Mathematical Journal, vol.15, no.2, pp.1-11, 2022 (Scopus)
- Publication Type: Article / Article
- Volume: 15 Issue: 2
- Publication Date: 2022
- Doi Number: 10.32513/asetmj/19322008213
- Journal Name: Advanced Studies: Euro-Tbilisi Mathematical Journal
- Journal Indexes: Scopus
- Page Numbers: pp.1-11
- Keywords: asymptotic curve, geodesic curve, line of curvature, Minkowski space, surface pencil
- Ondokuz Mayıs University Affiliated: Yes
Abstract
The adjoint curve of any Frenet curve r=r(s) is defined as the integral of binormal vector with any parameter s, of a curve r. In this paper,we analyzed the problem of finding a surfaces pencil through a given the spacelike adjoint curve as an asymptotic curve, geodesic or a line of curvature in Minkowski 3-space, respectively. We find necessary and sufficient condition for a surface pencil possessing the spacelike adjoint curve as an asymptotic curve, geodesic or line of curvature. We illustrate this method by presenting some examples.