2022/07/19 by Cortés, Vicente, Hasegawa, Kazuyuki · 1 citation
#53C10 #53C26 #53C56 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2207.09013
Given a hypercomplex manifold with a rotating vector field (and additional data), we construct a conical hypercomplex manifold. As a consequence, we associate a quaternionic manifold to a hypercomplex manifold of the same dimension with a rotating vector field. This is a generalization of the HK/QK-correspondence. As an application, we show that a quaternionic manifold can be associated to a conical special complex manifold of half its dimension. Furthermore, a projective special complex manifold (with a canonical c-projective structure) associates with a quaternionic manifold. The latter is a generalization of the supergravity c-map. We do also show that the tangent bundle of any special complex manifold carries a canonical Ricci-flat hypercomplex structure, thereby generalizing the rigid c-map.