Slant helices in three dimensional lie groups

TL;DR

This paper introduces the concept of slant helices within three-dimensional Lie groups equipped with a bi-invariant metric, providing characterizations and exploring their relations with involutes and spherical images.

Contribution

It defines slant helices in Lie groups and characterizes them, extending the geometric understanding of these curves in the context of Lie group theory.

Findings

Characterization of slant helices in three-dimensional Lie groups

Relations between slant helices and their involutes

Connections with spherical images

Abstract

In this paper, we define slant helices in three dimensional Lie Groups with a bi-invariant metric and obtain a characterization of slant helices. Moreover, we give some relations between slant helices and their involutes, spherical images.