Homogeneous Riemannian Structures in Thurston Geometries and Contact Riemannian Geometries

Year 2024, Volume: 17 Issue: 2, 559 - 659, 27.10.2024

Jun-ichi Inoguchi

https://doi.org/10.36890/iejg.1464086

Abstract

We give explicit parametrizations for all the homogeneous Riemannian structures on model spaces of Thurston geometry. As an application, we give all the homogeneous contact metric structures on $3$-dimensional Sasakian space forms.

Keywords

Homogeneous structures, Thurston geometry, Sasakian manifolds, Ambrose-Singer connections

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