# Cohomogeneity one conformal actions on the three-dimensional essential Riemannian spaces

## TL;DR

This paper classifies cohomogeneity one conformal group actions on three-dimensional essential Riemannian spaces, identifying all such group representations and orbit structures up to conformal equivalence.

## Contribution

It provides a complete classification of cohomogeneity one conformal actions and their orbit structures on three-dimensional essential Riemannian spaces.

## Key findings

- All connected Lie group actions of cohomogeneity one or zero are characterized.
- Orbits are classified up to conformal equivalence.
- Representations of these groups are determined up to conjugacy.

## Abstract

The aim of this paper is to classify the cohomogeneity one conformal actions on the three-dimensional essential Riemannian spaces, up to orbit equivalence. Among other results, the representations of all connected Lie groups acting with cohomogeneity one or zero within the full conformal group of a given three-dimensional essential Riemannian space are determined, up to conjugacy, and the orbits are specified up to conformal equivalence.