Open Access
June, 2000 Quaternionic Maps Between Hyperkähler Manifolds
Jingyi Chen, Jiayu Li
J. Differential Geom. 55(2): 355-384 (June, 2000). DOI: 10.4310/jdg/1090340881


Quaternionic maps (Q-maps) between hyperkähler manifolds are quaternionic analogue of Cauchy-Riemann equations between Kähler manifolds. We provide a necessary and sufficient condition on when a quaternionic map becomes holomorphic with respect to some complex structures in the hyperkähler 2-spheres, and give examples of Q-maps which cannot be holomorphic. When the domain is real 4-dimensional, we analyze the structure of the blow-up set of a sequence of Q-maps, and show that the singular set of a stationary $Q$-map is $\mathcal{H}^1$-rectifiable.


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Jingyi Chen. Jiayu Li. "Quaternionic Maps Between Hyperkähler Manifolds." J. Differential Geom. 55 (2) 355 - 384, June, 2000.


Published: June, 2000
First available in Project Euclid: 20 July 2004

zbMATH: 1308.53072
MathSciNet: MR1847314
Digital Object Identifier: 10.4310/jdg/1090340881

Rights: Copyright © 2000 Lehigh University

Vol.55 • No. 2 • June, 2000
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