Surface family with a common involute asymptotic curve

BAYRAM E., Bilici M.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, vol.13, no.5, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 5
  • Publication Date: 2016
  • Doi Number: 10.1142/s0219887816500626
  • Journal Name: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Involute curve, parametric surface, asymptotic curve, Frenet frame, PARAMETRIC REPRESENTATION, MINKOWSKI 3-SPACE, PENCIL, CURVATURE, LINE
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

We construct a surface family possessing an involute of a given curve as an asymptotic curve. We express necessary and sufficient conditions for that curve with the above property. We also present natural results for such ruled surfaces. Finally, we illustrate the method with some examples, e.g. circles and helices as given curves.