ON THE EVOLUTE OFFSETS OF RULED SURFACES USING THE DARBOUX FRAME


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ŞENTÜRK G. Y. , YÜCE S.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, vol.68, no.2, pp.1256-1264, 2019 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 68 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.31801/cfsuasmas.516604
  • Journal Name: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
  • Journal Indexes: Emerging Sources Citation Index, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1256-1264

Abstract

In this study, using Darboux frame {T, g, n} of ruled surface phi(s, v), the evolute offsets phi*(s, v) with Darboux frame {T*, g*, n*} of phi(s, v ) are defined. Characteristic properties of phi*(s,v) as a striction curve, distribution parameter and orthogonal trajectory are investigated using the Darboux frame. The distribution parameters of ruled surfaces phi*(T*), and phi*(g*) phi*(n*) are given. By using Darboux frame of the surfaces we have given the relations between the instantaneous Pfaffian vectors of motions H/H' and H*/H*' where H = {T, g, n} be the moving space along the base curve of phi(s,v), H* = {T*, g*, n*} be the moving space along the base curve of phi* (s, v), H' and H*' be fixed Euclidean spaces.