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H-anti-invariant submersions from almost quaternionic Hermitian manifolds. (English) Zbl 1458.53039

Summary: As a generalization of anti-invariant Riemannian submersions and Lagrangian Riemannian submersions, we introduce the notions of h-anti-invariant submersions and h-Lagrangian submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds. We obtain characterizations and investigate some properties: the integrability of distributions, the geometry of foliations, and the harmonicity of such maps. We also find a condition for such maps to be totally geodesic and give some examples of such maps. Finally, we obtain some types of decomposition theorems.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
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