Swann, Andrew Aspects symplectiques de la géométrie quaternionique. (Symplectic aspects of quaternionic geometry). (French) Zbl 0661.53023 C. R. Acad. Sci., Paris, Sér. I 308, No. 7, 225-228 (1989). 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. Cited in 2 ReviewsCited in 17 Documents MSC: 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53B35 Local differential geometry of Hermitian and Kählerian structures Keywords:fundamental 4-form; quaternion-Hermitian manifold; Quaternionic Kähler manifolds PDF BibTeX XML Cite \textit{A. Swann}, C. R. Acad. Sci., Paris, Sér. I 308, No. 7, 225--228 (1989; Zbl 0661.53023) OpenURL