Stationary acceleration of Frenet curves

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Abazari N., Bohner M., Sager I., YAYLI Y.

JOURNAL OF INEQUALITIES AND APPLICATIONS, vol.2017, 2017 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 2017
  • Publication Date: 2017
  • Doi Number: 10.1186/s13660-017-1354-7
  • Journal Name: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: stationary acceleration, spherical general helix, bi-invariant metric, Frenet elements, Minkowski space
  • Ankara University Affiliated: Yes

Abstract

In this paper, the stationary acceleration of the spherical general helix in a 3-dimensional Lie group is studied by using a bi-invariant metric. The relationship between the Frenet elements of the stationary acceleration curve in 4-dimensional Euclidean space and the intrinsic Frenet elements of the Lie group is outlined. As a consequence, the corresponding curvature and torsion of these curves are computed. In Minkowski space, for the curves on a timelike surface to have a stationary acceleration, a necessary and sufficient condition is refined.