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January 2021 The quaternionic/hypercomplex-correspondence
Vicente Cortés, Kazuyuki Hasegawa
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Osaka J. Math. 58(1): 213-238 (January 2021).


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.


We thank Aleksandra Borówka and Henrik Winther for discussions. Research by the first author is partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC 2121 Quantum Universe - 390833306. This paper was prepared during the second author's stay at Universität Hamburg on his sabbatical leave (April 2018 - March 2019). He would like to thank the Department of Mathematics of Universität Hamburg for the hospitality. His research is partially supported by JSPS KAKENHI Grant Number 18K03272.


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Vicente Cortés. Kazuyuki Hasegawa. "The quaternionic/hypercomplex-correspondence." Osaka J. Math. 58 (1) 213 - 238, January 2021.


Received: 8 May 2019; Revised: 15 October 2019; Published: January 2021
First available in Project Euclid: 9 May 2021

Primary: 53C10
Secondary: 53C26 , 53C56

Rights: Copyright © 2021 Osaka University and Osaka City University, Departments of Mathematics


Vol.58 • No. 1 • January 2021
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