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Quaternionic reduction and quaternionic orbifolds. (English) Zbl 0628.53060
An analogue of the process of symplectic reduction is defined for quaternionic Kähler manifolds. Certain features of the process are explored. In each dimension 4n, \(n>1\), the construction yields an infinite family of compact, simply-connected Riemannian orbifolds which have \(Sp_ 1Sp_ n\) holonomy and are not locally symmetric. In dimension 4, it yields infinite family of compact, simply-connected Riemannian orbifolds (“weighted” complex projective planes) which are Einstein, self-dual and of positive scalar curvature. This contrasts interestingly with a result of N. Hitchin in the non-singular case

53C55 Global differential geometry of Hermitian and Kählerian manifolds
53B35 Local differential geometry of Hermitian and Kählerian structures
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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