The quaternionic/hypercomplex-correspondence

12 Apr 2019  ·  Cortés Vicente, Hasegawa Kazuyuki ·

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. read more

PDF Abstract
No code implementations yet. Submit your code now

Categories


Differential Geometry