A New Version of Fermi Walker Derivative with Constant Energy for Normal Image of Slant Helix in the Lie Groups

Abstract

Fermi–Walker derivative and energy of curves play an important role in sensible guidelines. In this study we formulate a new energy for Fermi–Walker (FW) derivative of normal spherical image by using FW parallelism in Lie groups. By means of innovative illustration, we get new necessary and sufficient condition for the given field to be FW parallel. We give some partial differential equations. Moreover, we have some energy construction for normal spherical image in Lie groups. © 2018, Foundation for Scientific Research and Technological Innovation.