Constructions of Frenet Curves with respect to Semi-Symmetric Metric Connection

TL;DR

This paper develops a method to construct Frenet frames and curvatures of curves in 3D manifolds using semi-symmetric metric connections, with examples in Euclidean, Sasakian, and Kenmotsu manifolds.

Contribution

It introduces a novel approach to Frenet curve construction via semi-symmetric metric connections in various geometric manifolds.

Findings

Frenet frames constructed using semi-symmetric metric connections

Explicit examples in Euclidean, Sasakian, and Kenmotsu manifolds

New insights into curve geometry in specialized manifolds

Abstract

Using a semi-symmetric metric connection, we construct Frenet frame and curvatures of curves in 3-dimensional manifolds and give examples of semi-symmetric Frenet curves in Euclidean, Sasakian and Kenmotsu manifolds.