Detecting quaternionic maps between hyperkähler manifolds. (English) Zbl 1308.53072

Chen, Jingyi; Li, Jiayu

Commun. Math. Stat. 1, No. 3, 305-314 (2013).

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

Keywords:

harmonic maps; hyper-Kähler manifolds; quaternionic maps; Weitzenböck formula

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