Invariant metrics on lie groups : bi-invariance and one-parametre subgroups

Invariant metrics on lie groups bi-invariance and one-parametre subgroups

We show that an admissible left-invariant geodetic metric on a connected Lie group is bi-invariant if and only if every one-parametre subgroup t 7→ exp(tX) is a geodesic.

Bibliographic Details
Main Author:	Purho, Valto
Other Authors:	Faculty of Sciences, Matemaattis-luonnontieteellinen tiedekunta, Department of Mathematics and Statistics, Matematiikan ja tilastotieteen laitos, University of Jyväskylä, Jyväskylän yliopisto
Format:	Master's thesis
Language:	eng
Published:	2022
Subjects:	Mathematics Matematiikka 4041 matematiikka Lien ryhmät geometria mathematics Lie groups geometry
Online Access:	https://jyx.jyu.fi/handle/123456789/93493

Description
Summary:	We show that an admissible left-invariant geodetic metric on a connected Lie group is bi-invariant if and only if every one-parametre subgroup t 7→ exp(tX) is a geodesic.