# 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.
Document type :
Journal articles
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https://hal-cea.archives-ouvertes.fr/cea-00823343
Contributor : Bruno Savelli <>
Submitted on : Wednesday, January 13, 2021 - 4:56:03 PM
Last modification on : Wednesday, April 14, 2021 - 12:12:05 PM
Long-term archiving on: : Wednesday, April 14, 2021 - 7:04:16 PM

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cort1.pdf
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### Identifiers

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

### Citation

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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