Completeness in supergravity constructions

Details Completeness in supergravity constructions Completeness in supergravity constructions

2011-01-26

arxiv.org/abs/1101.5103v1

Physics

High Energy Physics

High Energy Physics - Theory

29 pages

Scientific paper

We prove that the supergravity r- and c-maps preserve completeness. As a consequence, any component H of a hypersurface {h=1} defined by a homogeneous cubic polynomial such that -d^2 h is a complete Riemannian metric on H defines a complete projective special Kahler manifold and any complete projective special Kahler manifold defines a complete quaternionic Kahler manifold of negative scalar curvature. We classify all complete quaternionic Kahler manifolds of dimension less or equal to 12 which are obtained in this way and describe some complete examples in 16 dimensions.

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