Legendre Trajectories of Trans-$S$-Manifolds

TL;DR

This paper studies Legendre trajectories in trans-$S$-manifolds, providing curvature characterizations, classification theorems, and analysis of special Legendre curves with linearly dependent Frenet frames.

Contribution

It introduces new curvature characterizations and classification results for Legendre trajectories in trans-$S$-manifolds, expanding understanding of their geometric properties.

Findings

Curvature characterizations of Legendre trajectories

Classification theorem for these curves

Analysis of Legendre curves with linearly dependent Frenet frames

Abstract

In this paper, we consider Legendre trajectories of trans-$S$-manifolds. We obtain curvature characterizations of these curves and give a classification theorem. We also investigate Legendre curves whose Frenet frame fields are linearly dependent with certain combination of characteristic vector fields of the trans-$S$-manifold.