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Aspects symplectiques de la géométrie quaternionique. (Symplectic aspects of quaternionic geometry). (French) Zbl 0661.53023

The vanishing of the exterior derivative of the fundamental 4-form \(\Omega\) of a quaternion-Hermitian manifold M, dim \(M\geq 12\), implies that \(\Omega\) is parallel. Quaternionic Kähler manifolds are included in the theory of hyperKähler manifolds in such a way that generalised symplectic reductions are preserved.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53B35 Local differential geometry of Hermitian and Kählerian structures
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