Normal and tangent maps to frontals

TL;DR

This paper introduces the concept of frontals in Euclidean space and investigates their normal and tangent maps, exploring both geometric and dynamical properties, and analyzing parallels of tangent maps under certain conditions.

Contribution

It presents a new framework for frontals and studies their normal and tangent maps, including their equivalence under parallels, which advances understanding of their geometric and dynamical behavior.

Findings

Normal and tangent maps to frontals are characterized.

Parallels of tangent maps are right equivalent under natural conditions.

The study links geometric and dynamical aspects of frontals.

Abstract

The notion of frontals in Euclidean space is introduced and the normal and tangent maps to frontals are studied for both geometrical and dynamical aspects of frontals. Moreover we observe that parallels of the tangent map to a frontal curve is right equivalent to the tangent map of a frontal curve under some natural conditions.