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2023•arXiv (Cornell University)Open access

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

Yu Ohno

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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.

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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.

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Available 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.

Key concepts: Homogeneous, Work (physics), Physics, Combinatorics, Mathematics, Quantum mechanics

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