The darboux trihedrons of regular curves on a regular time-like surface

In this work, we study Differential Geometry in the Minkowski 3-space R3 1 of the curves on a time-like regular surface by using parameter curves which are not perpendicular to each other. The aim of this study is to investigate the formulae between the Darboux Vectors of the time-like curve (c) , the time-like parameter curve (c1 ) and the space-like parameter curve (c2 ) which are not intersecting perpendicularly.