Completeness in supergravity constructions

Abstract

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.

29 pages

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Cited by in corpus (25)

• Quaternionic Kähler metrics associated with special Kähler manifolds
• Twist geometry of the c-map
• Para-Sasaki-like Riemannian manifolds and new Einstein metrics
• Black string first order flow in N=2, d=5 abelian gauged supergravity
• Special Geometry, Hessian Structures and Applications
• Classification of complete projective special real surfaces
• Symmetries of quaternionic Kähler manifolds with $S^1$-symmetry
• Toric geometry of $G_2$-manifolds
• Hyperbolic evolution equations, Lorentzian holonomy, and Riemannian generalised Killing spinors
• Pseudo-Kähler and pseudo-Sasaki structures on Einstein solvmanifolds
• Non-extremal black holes from the generalised r-map
• ASK/PSK-correspondence and the r-map
• Construction of projective special Kähler manifolds
• Four-dimensional geometric supergravity and electromagnetic duality: a brief guide for mathematicians
• The c-map as a functor on certain variations of Hodge structure
• Five-dimensional Nernst branes from special geometry
• Complete quaternionic Kähler manifolds with finite volume ends
• S-duality and the universal isometries of instanton corrected q-map spaces
• A class of locally inhomogeneous complete quaternionic Kähler manifolds
• Limit geometry of complete projective special real manifolds
• Special homogeneous surfaces
• Symmetries of one-loop deformed q-map spaces
• An analogue of the Gibbons-Hawking Ansatz for quaternionic Kähler spaces
• Special Geometry of Euclidean Supersymmetry IV: the local c-map
• S-duality and the universal isometries of q-map spaces