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

Swann, Andrew

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.

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