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<p>This paper classifies homogeneous Riemannian structures on 3-dimensional Lie groups with non-locally symmetric, left-invariant metrics. Together with existing classifications, our results provide a full characterization of homogeneous Riemannian structures on all 3-dimensional homogeneous Riemannian spaces. Furthermore, we present two applications of this classification to contact Riemannian geometry and CR geometry.</p>

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Homogeneous structures of 3-dimensional Lie groups

  • 期刊论文

  • 发表日期：

    2026年7月13日

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  • Jun-ichi Inoguchi,
  • Yu Ohno

摘要

This paper classifies homogeneous Riemannian structures on 3-dimensional Lie groups with non-locally symmetric, left-invariant metrics. Together with existing classifications, our results provide a full characterization of homogeneous Riemannian structures on all 3-dimensional homogeneous Riemannian spaces. Furthermore, we present two applications of this classification to contact Riemannian geometry and CR geometry.