Loxodromes on twisted surfaces in Lorentz–Minkowski 3-space

Abstract

In this paper, first, we give the general formulas according to first fundamental form of a surface for different types of loxodromes, meridians and surfaces in [Formula: see text]. After that, we obtain the differential equations of loxodromes on Type-I, Type-II and Type-III twisted surfaces in [Formula: see text] and also, we state a theorem which generalizes the differential equations of different types of loxodromes on the twisted surfaces for a special case. Finally, we provide several examples for visualizing our obtained results and draw our loxodromes and meridians on twisted surfaces with the aid of Mathematica.