Frenet frames and invariants of timelike ruled surfaces

Önder M., UĞURLU H. H.

Ain Shams Engineering Journal, vol.4, no.3, pp.507-513, 2013 (Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 4 Issue: 3
  • Publication Date: 2013
  • Doi Number: 10.1016/j.asej.2012.10.003
  • Journal Name: Ain Shams Engineering Journal
  • Journal Indexes: Scopus
  • Page Numbers: pp.507-513
  • Keywords: Minkowski 3-space, Timelike ruled surface, Curvatures
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

In this study we give the Frenet frames and Frenet invariants of timelike ruled surfaces. We show that a timelike ruled surface and its directing cone have the same base of Frenet frame. We define instantaneous rotation vectors of the Frenet frames of timelike ruled surfaces. Also we prove the Chasles Theorem for timelike ruled surfaces. © 2012 Ain Shams University. Production and hosting by Elsevier B.V. All rights reserved.