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 ⊂ 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 ⊂ 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 ⊂ M is a complex submanifold. Finally, we discuss how the existence of the Kähler structure on M′ is required by the consistency of spontaneous $${\mathcal{N} = 2}$$ to $${\mathcal{N} = 1}$$ supersymmetry breakin