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On certain Kähler quotients of quaternionic Kähler manifolds

Abstract : We prove that, given a certain isometric action of a two-dimensional Abelian group A on a quaternionic Kähler manifold M which preserves a submanifold N\subset M, the quotient M'=N/A has a natural Kähler structure. We verify that the assumptions on the group action and on the submanifold N\subset M are satisfied for a large class of examples obtained from the supergravity c-map. In particular, we find that all quaternionic Kähler manifolds M in the image of the c-map admit an integrable complex structure compatible with the quaternionic structure, such that N\subset M is a complex submanifold. Finally, we discuss how the existence of the Kähler structure on M' is required by the consistency of spontaneous {\cal N}=2 to {\cal N}=1 supersymmetry breaking.
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Contributor : Bruno Savelli <>
Submitted on : Thursday, May 16, 2013 - 4:28:29 PM
Last modification on : Monday, February 10, 2020 - 6:13:39 PM

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  • HAL Id : cea-00823343, version 1
  • ARXIV : 1111.0679



V. Cortés, J. Louis, P. Smyth, H. Triendl. On certain Kähler quotients of quaternionic Kähler manifolds. Communications in Mathematical Physics, Springer Verlag, 2013, 317, pp.787-816. ⟨cea-00823343⟩



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