On the restricted conformal group of the (1+n)-Einstein static universe

TL;DR

This paper constructs explicit models for the restricted conformal group of the (1+n)-Einstein static universe and classifies all conformal Lorentz manifolds with maximal restricted conformal group dimension.

Contribution

It provides explicit models for the restricted conformal group and classifies manifolds with maximal conformal symmetry in the Einstein static universe setting.

Findings

Explicit models for the restricted conformal group and its universal cover.

Classification of conformal Lorentz manifolds with maximal restricted conformal group.

Identification of the Einstein static universe and its quotients as maximal cases.

Abstract

Explicit models for the restricted conformal group of the Einstein static universe of dimension greater than two and for its universal covering group are constructed. Based on these models, as an application we determine all oriented and time-oriented conformal Lorentz manifolds whose restricted conformal group has maximal dimension. They amount to the Einstein static universe itself and two countably infinite series of its compact quotients.