Detecting quaternionic maps between hyperkähler manifolds. (English) Zbl 1308.53072
Summary: For a harmonic map between two hyper-Kähler manifolds, we prove a Weitzenböck type formula for the defining quantity of quaternionic maps, and apply it to harmonic morphisms. We also provide a sufficient and necessary condition for a smooth map being quaternionic.
MSC:
| 53C26 | Hyper-Kähler and quaternionic Kähler geometry, “special” geometry |
| 53C43 | Differential geometric aspects of harmonic maps |
References:
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