Homogeneous Structures on $\mathbb{S}^2\times\mathbb{R}$ and $\mathbb{H}^2\times\mathbb{R}$

Yu Ohno

Homogeneous Structures on $\mathbb{S}^2\times\mathbb{R}$ and $\mathbb{H}^2\times\mathbb{R}$

Differential Geometry 2023-07-12 v1

Authors: Yu Ohno

Abstract

We determine all the homogeneous structure tensors on $\mathbb{S}^2\times\mathbb{R}$ and $\mathbb{H}^2\times\mathbb{R}$ . This work together with previous articles yields a complete classification of all the homogeneous structure tensors on three-dimensional homogeneous Riemannian manifolds.

Keywords

holonomy

Cite

@article{arxiv.2307.05030,
  title  = {Homogeneous Structures on $\mathbb{S}^2\times\mathbb{R}$ and $\mathbb{H}^2\times\mathbb{R}$},
  author = {Yu Ohno},
  journal= {arXiv preprint arXiv:2307.05030},
  year   = {2023}
}

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