nLab locally Klein geometry

Idea

Generalising a Klein geometry, a locally Klein geometry is a triple $(\Gamma, G,H)$ where $G/H$ is a Klein geometry (not necessarily connected) and $\Gamma \subset G$ is a discrete subgroup acting by left multiplication on the coset space $G/H$ as a group of covering transformations with the double coset space, $\Gamma \backslash G/H$, connected (Sharpe 97, Def. 3.10, Sharpe 02, Def. 2.7).

Related concepts

• Clifford-Klein form

References

• Richard Sharpe, Differential geometry: Cartan’s generalization of Klein’s Erlangen program, Graduate Texts in Mathematics, vol. 166, Springer-Verlag, 1997.

• Richard Sharpe, An introduction to Cartan Geometries, in: Jan Slovák, Martin Čadek (eds.): Proceedings of the 21st Winter School “Geometry and Physics”. Circolo Matematico di Palermo, Palermo, 2002. Rendiconti del Circolo Matematico di Palermo, Serie II, Supplemento No. 69. pp. [61]–75 (EuDML)