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H-anti-invariant submersions from almost quaternionic Hermitian manifolds

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Abstract

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.

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Authors and Affiliations

  1. Division of General Mathematics, University of Seoul, Room 4-107, Changgong Hall, Seoul, 02504, Republic of Korea

    Kwang-Soon Park

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  1. Kwang-Soon Park
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Correspondence to Kwang-Soon Park.

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Park, KS. H-anti-invariant submersions from almost quaternionic Hermitian manifolds. Czech Math J 67, 557–578 (2017). https://doi.org/10.21136/CMJ.2017.0143-16

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  • DOI: https://doi.org/10.21136/CMJ.2017.0143-16

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