Construction of the Frenet-Serret frame of a curve in 4D Galilean space and some applications


Yilmaz S.

INTERNATIONAL JOURNAL OF THE PHYSICAL SCIENCES, vol.5, no.8, pp.1284-1289, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 8
  • Publication Date: 2010
  • Journal Name: INTERNATIONAL JOURNAL OF THE PHYSICAL SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1284-1289
  • Keywords: Galilean space, Frenet-Serret frame, spherical curves, vector differential equation, SURFACES, HELICES
  • Dokuz Eylül University Affiliated: No

Abstract

In this work, first, we construct Frenet-Serret frame of a curve in the Galilean 4-space. As a result of this, we obtain the mentioned curve's Frenet-Serret equations. Then, we prove that tangent vector of a curve in Galilean 4-space satisfies a vector differential equation of fourth order. Additionally, some characterizations of Galilean spherical curves and an example of the main results are presented.