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On Certain Kahler Quotients of Quaternionic Kahler Manifolds

We prove that, given a certain isometric action of a two-dimensional Abelian group A on a quaternionic Kahler manifold M which preserves a submanifold N aS, M, the quotient M' = N/A has a natural Kahler structure. We verify that the assumptions on the group action and on the submanifold N aS, M are satisfied for a large class of examples obtained from the supergravity c-map. In particular, we find that all quaternionic Kahler manifolds M in the image of the c-map admit an integrable complex structure compatible with the quaternionic structure, such that N aS, M is a complex submanifold. Finally, we discuss how the existence of the Kahler structure on M' is required by the consistency of spontaneous to supersymmetry breaking.

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