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

Ali A. T., Turgut M.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.365, sa.2, ss.559-569, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 365 Sayı: 2
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1016/j.jmaa.2009.11.026
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.559-569
  • Anahtar Kelimeler: Classical differential geometry, Minkowski 3-space, Slant helix, Intrinsic equations, SPACE, CURVE
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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.