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arXiv · 1904.06056

The quaternionic/hypercomplex-correspondence

Vicente Cortés·Kazuyuki Hasegawa
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Abstract

Given a quaternionic manifold $M$ with a certain $\mathrm{U}(1)$-symmetry, we construct a hypercomplex manifold $M'$ 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.

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Vicente Cortés, Kazuyuki Hasegawa. 2019-04-12. The quaternionic/hypercomplex-correspondence. https://arxiv.org/abs/1904.06056

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