Legendre curves on 3-dimensional $C_{12}$-Manifolds

TL;DR

This paper investigates Legendre curves in 3-dimensional $C_{12}$-manifolds, focusing on their properties and classifying all biharmonic Legendre curves within these non-normal almost contact manifolds.

Contribution

It extends the study of Legendre curves to non-normal $C_{12}$-manifolds and provides a classification of biharmonic Legendre curves in this setting.

Findings

Classification of all biharmonic Legendre curves in $C_{12}$-manifolds

Extension of known results to non-normal almost contact manifolds

Insights into the geometry of Legendre curves in these manifolds

Abstract

Legendre curves play a very important and special role in geometry and topology of almost contact manifolds.There are certain results known for Legendre curves in 3-dimensional normal almost contact manifolds. The aim of this paper is to study Legendre curves of three-dimensional $C_{12}$-manifolds which are non-normal almost contact manifolds and classifying all biharmonic Legendre curves in these manifolds.