NEW CHARACTERIZATIONS OF SPACELIKE CURVES ON TIMELIKE SURFACES THROUGH THE LINK OF SPECIFIC FRAMES


Unluturk Y., Yilmaz S.

TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, vol.8, pp.330-340, 2018 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 8
  • Publication Date: 2018
  • Journal Name: TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.330-340
  • Keywords: Spacelike curve, Darboux frame, Darboux vector, Type-2 Bishop frame
  • Dokuz Eylül University Affiliated: Yes

Abstract

In this work, considering a regular spacelike curve on a smooth timelike surface in Minkowski 3-space, we investigate relations between the mentioned curve's Darboux and Bishop frames on the timelike surface. Next we obtain Darboux vector of the regular spacelike curve in terms of Bishop apparatus. Thereafter, translating the Darboux vector to the center of the unit sphere, we determine aforementioned spacelike curve. Moreover, we investigate this spherical image's Frenet-Serret and Bishop apparatus and illustrate our results with two examples.