Hokkaido Mathematical Journal

URAKAWA Hajime,

Projectively flat connections and flat connections on homogeneous spaces.

Hokkaido Mathematical Journal, 39 (2010) pp.139-155

Fulltext

PDF

Abstract

We show a correspondence between the set of all $G$-invariant projectively flat connections on a homogeneous space $M=G/K$, and the one of all $\widetilde{G}$-invariant flat connections on homogeneous spaces $\widetilde{M}=\widetilde{G}/K$, where $\widetilde{G}$ is a central extension of $G$ (Theorem 3.3).

MSC(Primary)
MSC(Secondary)53A15(MSC2000), 53C35(MSC2000), 53C42(MSC2000), 22E45(MSC2000)
Uncontrolled Keywordsprojectively flat connection; flat connection; reductive homogeneous space; symmetric space; simple Lie group;