Homogeneous structures of $3$-dimensional Lie groups
Differential Geometry
2025-01-22 v1
Abstract
We give a classification of homogeneous Riemannian structures on (non locally symmetric) -dimensional Lie groups equipped with left invariant Riemannian metrics. This work together with classifications due to previous works yields a complete classification of all the homogeneous Riemannian structures on homogeneous Riemannian -spaces. Two applications of the classification to contact Riemannian geometry and CR geometry are also given.
Cite
@article{arxiv.2501.11321,
title = {Homogeneous structures of $3$-dimensional Lie groups},
author = {Jun-ichi Inoguchi and Yu Ohno},
journal= {arXiv preprint arXiv:2501.11321},
year = {2025}
}
Comments
arXiv admin note: text overlap with arXiv:2408.01645