The quaternionic/hypercomplex-correspondence
Differential Geometry
2019-04-15 v1
Abstract
Given a quaternionic manifold with a certain -symmetry, we construct a hypercomplex manifold of the same dimension. This construction generalizes the quaternionic K\"ahler/hyper-K\"ahler-correspondence. As an example of this construction, we obtain a compact homogeneous hypercomplex manifold which does not admit any hyper-K\"ahler structure. Therefore our construction is a proper generalization of the quaternionic K\"ahler/hyper-K\"ahler-correspondence.
Cite
@article{arxiv.1904.06056,
title = {The quaternionic/hypercomplex-correspondence},
author = {Vicente Cortés and Kazuyuki Hasegawa},
journal= {arXiv preprint arXiv:1904.06056},
year = {2019}
}