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In this paper, we introduce hsR maps and ahsR maps from almost quaternionic Hermitian manifolds into Riemannian manifolds as a generalization of almost h-conformal semi-invariant submersions and conformal semi-invariant Riemannian maps. We give some examples of these maps and study their properties: the geometry of foliations, the integrability of distributions, the conditions for these maps to be harmonic or totally geodesic.

On the almost h-conformal semi-invariant Riemannian maps