Spherical Indicatrices of Involute of a Space Curve in Euclidean 3-Space

TL;DR

This paper investigates the properties of spherical indicatrices of involute space curves, especially when involved with helices and slant helices, and introduces new representations of these indicatrices.

Contribution

It provides new insights into the properties and representations of spherical indicatrices of involute curves, particularly in special cases involving helices and slant helices.

Findings

Spherical indicatrices exhibit specific properties when involute and evolute curves are helices or slant helices.

New representations of spherical indicatrices are introduced.

Characterizations of these indicatrices in special geometric configurations.

Abstract

In this work, we studied the properties of the spherical indicatrices of involute curve of a space curve and presented some characteristic properties in the cases that involute curve and evolute curve are slant helices and helices, spherical indicatrices are slant helices and helices and we introduced new representations of spherical indicatrices.