Quaternionic Structures in Mathematics and Physics

Pontecorvo, Massimiliano; Marchiafava, S.; Piccinni, Paolo

doi:10.1142/4709

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Holonomy groups of pseudo-quaternionic-Kählerian manifolds of non-zero scalar curvature

Bezvitnaya

2010

Ann Glob Anal Geom

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The holonomy group G of a pseudo-quaternionic-Kählerian manifold of signature (4r, 4s) with non-zero scalar curvature is contained in Sp(1) · Sp(r, s) and it contains Sp(1). It is proved that either G is irreducible, or s = r and G preserves an isotropic subspace of dimension 4r , in the last case, there are only two possibilities for the connected component of the identity of such G. This gives the classification of possible connected holonomy groups of pseudo-quaternionic-Kählerian manifolds of non-zero scalar curvature.

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