Complete quaternionic Kähler manifolds with finite volume ends
[Variétés quaternion-kählériennes complètes avec bouts de volume fini]
Cortés, Vicente1 ; Röser, Markus1 ; Thung, Daniel1
1 Department of Mathematics, University of Hamburg (Germany)
Annales de l'Institut Fourier, Online first, 47 p.

Nous construisons des exemples de variétés quaternion-kählériennes complètes avec un bout de volume fini, qui ne sont pas localement homogènes. Les variétés sont asphériques avec groupe fondamental qui est, à une extension cyclique infinie près, un produit semi-direct d’un réseau dans un groupe semi-simple avec un réseau dans un groupe de Heisenberg. Leur revêtement universel est une déformation de cohomogénéité 1 d’un espace symétrique de type non compact.

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.

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DOI : 10.5802/aif.3664
Classification : 53C26
Keywords: Quaternionic Kähler manifolds, $c$-map, One-loop deformation, Isometry groups, Cohomogeneity one.
Mot clés : Variétés quaternion-kählériennes, $c$-map, Déformation à une boucle, Groupes d’isométries, Cohomogénéité 1.

Cortés, Vicente 1 ; Röser, Markus 1 ; Thung, Daniel 1

1 Department of Mathematics, University of Hamburg (Germany) 
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Cortés, Vicente; Röser, Markus; Thung, Daniel. Complete quaternionic Kähler manifolds with finite volume ends. Annales de l'Institut Fourier, Online first, 47 p.

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