Slant curves in 3-dimensional normal almost paracontact metric manifolds

TL;DR

This paper investigates the curvature and torsion of slant Frenet and non-Frenet curves in 3D normal almost paracontact metric manifolds, providing new properties and illustrative examples.

Contribution

It introduces new properties of slant curves, including non-Frenet cases, in 3D normal almost paracontact metric manifolds, expanding understanding of their geometric behavior.

Findings

Derived curvature and torsion formulas for slant Frenet curves.

Established properties of non-Frenet slant curves with null tangents or normals.

Provided illustrative examples of the theoretical results.

Abstract

The presented paper is devoted to study the curvature and torsion of slant Frenet curves in 3-dimensional normal almost paracontact metric manifolds. Moreover, in this class of manifolds, properties of non- Frenet slant curves (with null tangents or null normals) are obtained. The achieved results are illustrated by examples.