Communications of the
Korean Mathematical Society CKMS

In this paper, h-quasi-hemi-slant submersions and almost h-quasi-hemi-slant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds are introduced. Fundamental results on h-quasi-hemi-slant submersions: the integrability of distributions, geometry of foliations and the conditions for such submersions to be totally geodesic are investigated. Moreover, some non-trivial examples of the h-quasi-hemi-slant submersion are constructed.

Keywords: Riemannian submersions, quaternionic Hermitian manifold, integrability, totally geodesic

MSC numbers: 53C26, 53B35