# Legendre curves and singularities of a ruled surface according to rotation minimizing frame

## TL;DR

This paper explores the geometry of Legendre curves on the unit tangent bundle using rotation minimizing frames, analyzes the singularities of associated ruled surfaces, and classifies these singularities.

## Contribution

It introduces a novel approach to studying ruled surface singularities via Legendre curves and RM vector fields, providing new classifications and insights.

## Key findings

- Singularities of ruled surfaces are classified.
- Legendre curves are characterized using RM vector fields.
- New geometric insights into ruled surface singularities.

## Abstract

In this paper, Legendre curves on unit tangent bundle are given using rotation minimizing (RM) vector fields. Ruled surfaces corresponding to these curves are represented. Singularities of these ruled surfaces are also analyzed and classifed.