Work

The quaternionic/hypercomplex-correspondence

Year: 2019

Type: article

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 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.

Source: Osaka City University (Osaka City University)

DOI: 10.48550/arxiv.1904.06056

Authors: Cortés, Vicente, Hasegawa, Kazuyuki

Institutions: Universität Hamburg, Kanazawa University

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Universität Hamburg, Japan Society for the Promotion of Science

Awards: G432818845, EXC 2121: Quantum Universe, The research of quaternionic manifolds by using subamnifold geometry