The quaternionic/hypercomplex-correspondence

Abstract

Given a quaternionic manifold $M$ with a certain $\mathrm{U}(1)$-symmetry, we construct a hypercomplex manifold $M^{\prime }$ of the same dimension. This construction generalizes the quaternionic Kähler/hyper-Kähler-correspondence. As an example of this construction, we obtain a compact homogeneous hypercomplex manifold which does not admit any hyper-Kähler structure. Therefore our construction is a proper generalization of the quaternionic Kähler/hyper-Kähler-correspondence.

References in corpus (1)

• HyperKahler and quaternionic Kahler manifolds with S^1-symmetries

Cited by in corpus (1)

• Curvature of quaternionic skew-Hermitian manifolds and bundle constructions