Detecting Quaternionic Maps Between Hyperkähler Manifolds

Abstract

For a harmonic map between two hyperkäher 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.

Keywords

Harmonic maps / Hyperkähler manifolds / Quaternionic maps / Weitzenböck formula

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