Spherical Indicatrices of a Bertrand Curve in Three Lie Groups

TL;DR

This paper introduces new representations of Bertrand curves in three Lie groups with bi-invariant metrics and explores their spherical indicatrices and related geometric relations.

Contribution

It provides novel representations of Bertrand curve pairs and analyzes their spherical indicatrices within the context of three-dimensional Lie groups.

Findings

New representations of Bertrand curve pairs in Lie groups

Relations between spherical indicatrices and curve representations

Enhanced understanding of Bertrand curves in geometric group theory

Abstract

In this paper, new representations of a Bertrand curve pair in three dimensional Lie groups with bi-invariant metric are given. Besides, the spherical indicatrices of a Bertrand curve pair are obtain and the relations between the spherical indicatrices and new representations of Bertrand curve pair are shown.