Complete quaternionic Kähler manifolds with finite volume ends

Abstract

We construct examples of complete quaternionic Kähler manifolds with an end of finite volume, which are not locally homogeneous. The manifolds are aspherical with fundamental group which is up to an infinite cyclic extension a semi-direct product of a lattice in a semi-simple group with a lattice in a Heisenberg group. Their universal covering is a cohomogeneity one deformation of a symmetric space of non-compact type.

39 pages; accepted for publication in Annales de l'institut Fourier. Various improvements based on suggestions of the anonymous referee, most notably in section 4.1. Matches version to be published modulo formatting

References in corpus (2)

• String loop corrected hypermultiplet moduli spaces
• HyperKahler and quaternionic Kahler manifolds with S^1-symmetries

Cited by in corpus (2)

• Quaternionic Kähler metrics associated to special Kähler manifolds with mutually local variations of BPS structures
• The c-map as a functor on certain variations of Hodge structure