# Surfaces of revolution of frontals in the Euclidean space

## TL;DR

This paper studies surfaces of revolution generated from frontals in Euclidean space, deriving their curvatures and invariants, and analyzing properties related to singularities and cones.

## Contribution

It introduces a framework for understanding surfaces of revolution of frontals via Legendre curves, including curvature formulas and singularity properties.

## Key findings

- Derived curvature formulas for surfaces of revolution of frontals.
- Characterized singularities and cone properties of these surfaces.
- Connected surface invariants to Legendre curve curvatures.

## Abstract

For Legendre curves, we consider surfaces of revolution of frontals. The surface of revolution of a frontal can be considered as a framed base surface. We give the curvatures and basic invariants for surfaces of revolution by using the curvatures of Legendre curves. Moreover, we give properties of surfaces of revolution with singularities and cones.