The Fermi derivative in the hypersurfaces

KARAKUŞ F., YAYLI Y.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, vol.12, no.1, 2015 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 1
  • Publication Date: 2015
  • Doi Number: 10.1142/s0219887815500024
  • Journal Name: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Fermi derivative, Fermi parallelism, non-rotating frame, hypersurface, Levi-Civita connection, Levi-Civita parallel, Frenet frame, Darboux frame, W-curve, curvature, torsion, CURVES
  • Ankara University Affiliated: Yes

Abstract

In this study, Fermi derivative and according to the derivative Fermi parallelism and non-rotating frame concepts are given on any hypersurface in En+1. Initially, Fermi derivative and non-rotating concepts are analyzed on any hypersurface in E-4. As an example, S-3 is taken instead of the hypersurface in E-4. Fermi derivative and non-rotating concepts are examined for S-3. Then a correlation is found between Fermi derivative and Levi-Civita derivative of any vector field in E-4. And then the concepts of Fermi derivative are generalized for n > 4 in En+1.