Position vector of a time-like slant helix in Minkowski 3-space

Ali A. T., Turgut M.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.365, no.2, pp.559-569, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 365 Issue: 2
  • Publication Date: 2010
  • Doi Number: 10.1016/j.jmaa.2009.11.026
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.559-569
  • Keywords: Classical differential geometry, Minkowski 3-space, Slant helix, Intrinsic equations, SPACE, CURVE
  • Dokuz Eylül University Affiliated: Yes

Abstract

In this paper, position vector of a time-like slant helix with respect to standard frame of Minkowski Space E-1(3) is studied in terms of Frenet equations. First, a vector differential equation of third order is constructed to determine position vector of an arbitrary time-like slant helix. In terms of solution, we determine the parametric representation of the slant helices from the intrinsic equations. Thereafter, we apply this method to find the representation of a time-like Salkowski and time-like anti-Salkowski curves as examples of a slant helices, by means of intrinsic equations. Moreover, we present some new characterizations of slant helices and illustrate some examples of our main results. (C) 2009 Elsevier Inc. All rights reserved.