Special curves in finsler space

Abstract

As one point moves along a curve, if the Frenet vectors are carried to the center of the unit Finsler sphere F S 2 at this point then these vectors trace curves on the F S 2 . These curves called as spherical images of the curve c. In this study, we investigate the Finslerian spherical images of any curve in Finsler space F 3 . Also, we obtain the Frenet-Serret formulas of these new curves in terms of Finsler invari-ants. Furthermore, these curves are exemplified using the Randers metric which is a special structure of the Finsler metric. Finally, these curves are illustrated on the F S 2 . © 2018, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved.