Cohomology of Quaternionic Foliations and Orbifolds

Abstract

Starting with a concise review of quaternionic geometry and quaternionic K{ä}hler manifolds, we define a transversely quaternionic K{ä}hler foliation. Then we formulate and prove the foliated versions of the now classical results of V.Y. Kraines and A. Fujiki on the cohomology of quaternionic K{ä}hler manifolds. Finally, as any orbifold can be realized as the leaf space of a suitably defined Riemannian foliation we reformulate our results for quaternionic orbifolds.