Homogeneous Riemannian structures in dimension three

In this note, we determine all the homogeneous structures on non-symmetric three-dimensional Riemannian Lie groups. We show that a non-symmetric three-dimensional Riemannian Lie group admits a non-canonical homogeneous structure if and only if its isometry group has dimension four.

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Bibliographic Details
Published in:	Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 117; no. 2
Main Authors:	Calviño-Louzao, E., Ferreiro-Subrido, M., García-Río, E., Vázquez-Lorenzo, R.
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01-04-2023 Springer Nature B.V
Subjects:	Applications of Mathematics Homogeneous structure Lie groups Mathematical and Computational Physics Mathematics Mathematics and Statistics Original Paper Theoretical Homogeneous structure 53C30 Homogeneous space 53C25 53C55
Online Access:	Get full text
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Description
Summary:	In this note, we determine all the homogeneous structures on non-symmetric three-dimensional Riemannian Lie groups. We show that a non-symmetric three-dimensional Riemannian Lie group admits a non-canonical homogeneous structure if and only if its isometry group has dimension four.
ISSN:	1578-7303 1579-1505
DOI:	10.1007/s13398-023-01404-y