On geometry of spherical image in Minkowski space-time with timelike type-2 parallel transport frame

Authors

Solouma Solouma, Beni-Suef University
Ibrahim Al-Dayel, Al Imam Mohammad Ibn Saud Islamic University

Abstract

In this paper, we investigate a different type of the parallel transport frame in 3-dimensional Minkowski space R^3_1 by using the binormal vector field of a timelike regular curve as common vector field to introduce, and we recall this frame as " timelike type-2 parallel transport frame". Also, we present new spherical images and call them as timelike type-2 parallel transport spherical images by translating the induced frame vectors to the center of unit Lorentzian sphere in 3-dimensional Minkowski space R^3_1. Additionally, we obtain the Frenet apparatus of these new spherical images in terms of base curves timelike type-2 parallel transport invariants. Finally, interesting relations are expressed and illustrate an example of the results.

Recommended Citation

Solouma, Solouma and Al-Dayel, Ibrahim (2020). On geometry of spherical image in Minkowski space-time with timelike type-2 parallel transport frame, Applications and Applied Mathematics: An International Journal (AAM), Vol. 15, Iss. 1, Article 29.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss1/29