HOMOGENEOUS STRUCTURES ON S2×R AND H2×R

Yu Ohno

doi:10.21099/tkbjm/20234702239

Abstract

We determine all the homogeneous structure tensors on $\mathbf{S}^2 \times \mathbf{R}$ and $\mathbf{H}^2 \times \mathbf{R}$ . This work together with previous articles [1, 3, 4, 7, 8] yields a complete classification of all the homogeneous structure tensors on three-dimensional homogeneous Riemannian manifolds.

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Yu Ohno. "HOMOGENEOUS STRUCTURES ON $\mathbf{S}^2 \times \mathbf{R}$ AND $\mathbf{H}^2 \times \mathbf{R}$ ." Tsukuba J. Math. 47 (2) 239 - 246, December 2023. https://doi.org/10.21099/tkbjm/20234702239

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Received: 24 July 2023; Revised: 19 October 2023; Published: December 2023

First available in Project Euclid: 18 March 2024

Digital Object Identifier: 10.21099/tkbjm/20234702239

Subjects:

Primary: 53C30

Secondary: 53C25

Keywords: Ambrose-Singer connection , homogeneous space , homogeneous structure

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