On Legendre Curves in 3-Dimensional Normal Almost Paracontact Metric Manifolds

Abstract

The present paper is devoted to study the curvature and torsion of Frenet Legendre curves in 3-dimensional normal almost paracontact metric manifolds. Moreover, in this class of manifolds, properties of non-Frenet Legendre curves (with null tangents or null normals or null binormals) are obtained. Many examples of Legendre curves are constructed.Some of the present results are analogous to those obtained by the author in [10] for Frenet Legendre curves in 3-dimensional normal almost contact manifolds. Mathematics Subject Classification (2000). 53D15, 53C25.

Mechanical Equations on Slant Curves in 3-dimensional Normal Almost Paracontact Metric Manifolds

“…A semi-Riemannian metric g is said to be an associated metric if there exists a tensor ϕ of type (1,1), such that…”

“…They have a simple method to describe the model for mechanical systems. Welyczko generalized some of them to the case of 3-dimensional normal almost contact metric manifolds, especially, quasi-Sasakian manifolds [1]. Tripathi et al introduce the concept of ε-almost paracontact manifolds, and in particular, of ε-paraSasakian manifolds [2].…”

Curvature and torsion of a legendre curve in (e;d) Trans-Sasakian manifolds

“…Moreover J. Welyczko have studied Legendre curve on quasi Sasakian manifolds [15] and almost paracontact metric manifolds [16]. Motivated by these works, in this paper we study Legendre curves on 3-dimensional (ε, δ ) trans-Sasakian manifolds.…”

Some Classes of 3-Dimensional Normal Almost Paracontact Metric Manifolds

“…• β-para-Sasakian if and only if α = 0 and β = 0 and β is constant, in particular, para-Sasakian if β = −1 [15], [18],…”

“…Recently, J. We lyczko studied curvature and torsion of Frenet-Legendre curves in 3-dimensional normal almost paracontact metric manifolds [15]. The structures of some classes of 3-dimensional normal almost contact metric manifolds were studied in [9].…”