Frenet curves in 3-dimensional $ \delta $-Lorentzian trans Sasakian manifolds

<abstract><p>In this paper, we give some characterizations of Frenet curves in 3-dimensional $ \delta $-Lorentzian trans-Sasakian manifolds. We compute the Frenet equations and Frenet elements of these curves. We also obtain the curvatures of non-geodesic Frenet curves on 3-dimensional $ \delta $-Lorentzian trans-Sasakian manifolds. Finally, we give some results for these curves.</p></abstract>

On curves in 3-dimensional normal almost contact metric manifolds

The characterization of curves plays an important role in both geometry and topology of almost contact manifolds. Olszak found the equation [Formula: see text] on normal almost contact manifolds. The pair [Formula: see text] denotes the type of these manifolds. In this study, we obtained the curvatures of non-geodesic Frenet curves on [Formula: see text]-dimensional normal almost contact manifolds without neglecting [Formula: see text] and [Formula: see text], and provided the results of their characterization. We exemplified these results with examples.

On the Deformation Retractions of Frenet Curves in Minkowski 4 - Space

In this paper, the position vector equation of &nbsp;&nbsp;the Frenet curves with constant curvatures in Minkowski 4 -space has been presented. New types for retractions and deformation retracts of Frenet curves in &nbsp;are deduced. The relations between the Frenet apparatus of the Frenet curves before and after the deformation retracts are obtained.