Normal Fermi- Walker Derivative

Abstract

In this paper, first, we defined normal Fermi-Walker derivative and applied for adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame and Darboux vector of normal Fermi-Walker derivative by using normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are researched throughout curve for Frenet frame and Adapted frame. It is shown that vector field which take part in [13] is normal FermiWalker parallel in accordance with the normal Fermi-Walker derivative along the general helix. Also, we show that the Frenet frame is normal non-rotating frame in accordance with the normal Fermi-Walker derivative. Afterwards, we testified that the adapted frame is normal non-rotating frame throughout the general helix.