# On C-Parallel Legendre Curves in Non-Sasakian Contact Metric Manifolds

## TL;DR

This paper characterizes C-parallel and C-proper Legendre curves in non-Sasakian contact metric manifolds, providing curvature conditions and examples to deepen understanding of their geometric properties.

## Contribution

It introduces new curvature characterizations of Legendre curves with C-parallel or C-proper mean curvature vectors in non-Sasakian contact metric manifolds, including explicit examples.

## Key findings

- Curvature conditions for C-parallel Legendre curves
- Curvature conditions for C-proper Legendre curves
- Explicit examples satisfying the conditions

## Abstract

In $(2n+1)$-dimensional non-Sasakian contact metric manifolds, we consider Legendre curves whose mean curvature vector fields are $\mathcal{C}$-parallel or $\mathcal{C}$-proper in the tangent or normal bundles. We obtain the curvature characterizations of these curves. Moreover, we give some examples of these kinds of curves which satisfy the conditions of our results.