Homogeneous structures of $3$-dimensional Sasakian space forms

TL;DR

This paper provides explicit parametrizations for all homogeneous contact Riemannian structures on three-dimensional Sasakian space forms, enhancing understanding of their geometric configurations.

Contribution

It introduces explicit parametrizations for all such structures, offering a comprehensive classification in the three-dimensional case.

Findings

Explicit parametrizations for all homogeneous structures identified

Complete classification of 3D Sasakian space forms achieved

Enhanced understanding of geometric configurations in contact Riemannian structures

Abstract

We give explicit parametrizations for all the homogeneous contact Riemannian structures on $3$-dimensional Sasakian space forms.