A new method for inextensible flows of timelike curves in 4-dimensional LP-Sasakian manifolds

Inextensible flows of timelike curves plays an important role in practical applications. In this paper, we construct a new method for inextensible flows of timelike curves in a conformally flat, quasi conformally flat and conformally symmetric 4-dimensional LPSasakian manifold. With this new representation, we derive the necessary and sufficient condition for the given curve to be the inextensible flow. By using curvature tensor field, we give some characterizations for curvatures of a timelike curve in a conformally flat, quasi conformally flat and conformally symmetric 4-dimensional LP-Sasakian manifold. Finally, we obtain flows of some associated curves of timelike curves.