## Journal of Differential Geometry

### Quaternionic Maps Between Hyperkähler Manifolds

#### Abstract

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.

#### Article information

Source
J. Differential Geom., Volume 55, Number 2 (2000), 355-384.

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090340881

Digital Object Identifier
doi:10.4310/jdg/1090340881

Mathematical Reviews number (MathSciNet)
MR1847314

Zentralblatt MATH identifier
1308.53072

#### Citation

Chen, Jingyi; Li, Jiayu. Quaternionic Maps Between Hyperkähler Manifolds. J. Differential Geom. 55 (2000), no. 2, 355--384. doi:10.4310/jdg/1090340881. https://projecteuclid.org/euclid.jdg/1090340881