Characterization of Legendre curves in quasi-Sasakian pseudo-metric 3-manifolds

TL;DR

This paper explores the geometric properties of Legendre curves within 3-dimensional quasi-Sasakian pseudo-metric manifolds, providing spherical characterizations and analyzing null Legendre curves.

Contribution

It introduces new spherical characterizations of Legendre and null Legendre curves in quasi-Sasakian pseudo-metric 3-manifolds.

Findings

Spherical characterization of Legendre curves

Characterization of null Legendre curves

Insights into geometric structures of quasi-Sasakian manifolds

Abstract

The main purpose of this paper is to present the spherical characterization of Legendre curves in $3$-dimensional quasi-Sasakian pseudo-metric manifolds. Furthermore, null Legendre curves are also characterized in this class of manifold.