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H-anti-invariant submersions from almost quaternionic Hermitian manifolds

Kwang-Soon Park (2017)

Czechoslovak Mathematical Journal

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...

H-conformal anti-invariant submersions from almost quaternionic Hermitian manifolds

Kwang Soon Park (2020)

Czechoslovak Mathematical Journal

We introduce the notions of h-conformal anti-invariant submersions and h-conformal Lagrangian submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, anti-invariant submersions, h-anti-invariant submersions, h-Lagrangian submersion, conformal anti-invariant submersions. We investigate their properties: the integrability of distributions, the geometry of foliations, the conditions for such...

Homogeneous quaternionic Kähler structures on Alekseevskian 𝒲-spaces

Wafaa Batat, P. M. Gadea, Jaime Muñoz Masqué (2012)

Annales Polonici Mathematici

The homogeneous quaternionic Kähler structures on the Alekseevskian 𝒲-spaces with their natural quaternionic structures, each of these spaces described as a solvable Lie group, and the type of such structures in Fino's classification, are found.

Hyperholomorphic connections on coherent sheaves and stability

Misha Verbitsky (2011)

Open Mathematics

Let M be a hyperkähler manifold, and F a reflexive sheaf on M. Assume that F (away from its singularities) admits a connection ▿ with a curvature Θ which is invariant under the standard SU(2)-action on 2-forms. If Θ is square-integrable, such sheaf is called hyperholomorphic. Hyperholomorphic sheaves were studied at great length in [21]. Such sheaves are stable and their singular sets are hyperkähler subvarieties in M. In the present paper, we study sheaves admitting a connection with SU(2)-invariant...

Hyperkaehler metrics from projective superspace

Ulf Lindström (2007)

Archivum Mathematicum

This is a brief review of how sigma models in Projective Superspace have become important tools for constructing new hyperkähler metrics.

Hyperkähler manifolds

Nigel Hitchin (1991/1992)

Séminaire Bourbaki

Hypersurfaces with almost complex structures in the real affine space

Mayuko Kon (2007)

Colloquium Mathematicae

We study affine hypersurface immersions $f : M \to ℝ^{2 n + 1}$ , where M is an almost complex n-dimensional manifold. The main purpose is to give a condition for (M,J) to be a special Kähler manifold with respect to the Levi-Civita connection of an affine fundamental form.