An approach to characterizations of null curves lying in timelike ruled surfaces

Abstract

In physics literature, there is a crucial link of timelike ruled surfaces in which null curves lying with some subjects of general relativity such as the world lines of photon surfaces. Based upon this motivation, we try to see the mutual relations of null asymptotic lines and null lines of curvature in timelike ruled surfaces in dual Lorentzian 3-space D13. We suggest a system of differential equations featuring the relative characterizations of these geometric objects. Regarding to the solutions of the system, we contributed to the area by some geometric results linked to both null asymptotic lines and timelike ruled surfaces, and null lines of curvature and timelike ruled surfaces in the aforementioned space. For example, one of these results is to express the curve–surface pair in terms of Blaschke vectors. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.