Extended optical radial direction of optical motion with extended Darboux frame

Abstract

In this paper, we derive optical conditions for extended Darboux frame to make some optical motions such as uniformly optical accelerated motion, unchanged optical direction motion, and uniformly circular optical motion by using Fermi-Walker derivative. We also construct the new optical relations between the Fermi-Walker parallel transportation and these motions in 4-space. In other words, we obtain the applied geometric optical characterization for the uniformly optical accelerated motion, unchanged optical direction motion, and uniformly optical circular motion with extended Darboux frame in 4-space.