Slant null curves on normal almost contact B-metric 3-manifolds with parallel Reeb vector field

TL;DR

This paper investigates the properties of slant null curves on 3-dimensional normal almost contact B-metric manifolds with parallel Reeb vector fields, establishing conditions for their Frenet frames and providing explicit examples.

Contribution

It introduces a unique Frenet frame for non-geodesic slant null curves and determines when it is a Cartan Frenet frame, with explicit examples.

Findings

Existence of a unique Frenet frame for non-geodesic curves

Necessary condition for the Frenet frame to be a Cartan frame

Construction of explicit examples of slant null curves

Abstract

In this paper we study slant null curves with respect to the original parameter on 3-dimensional normal almost contact B-metric manifolds with parallel Reeb vector field. We prove that for non-geodesic such curves there exists a unique Frenet frame for which the original parameter is distinguished. Moreover, we obtain a necessary condition this Frenet frame to be a Cartan Frenet frame with respect to the original parameter. Examples of the considered curves are constructed.