Detecting Quaternionic Maps Between Hyperkähler Manifolds

Jingyi Chen; Jiayu Li

doi:10.1007/s40304-013-0016-4

Communications in Mathematics and Statistics ›› 2013, Vol. 1 ›› Issue (3) : 305 -314. DOI: 10.1007/s40304-013-0016-4

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Detecting Quaternionic Maps Between Hyperkähler Manifolds

Jingyi Chen ¹
, Jiayu Li ²^,³^,^b

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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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Jingyi Chen, Jiayu Li. Detecting Quaternionic Maps Between Hyperkähler Manifolds. Communications in Mathematics and Statistics, 2013, 1(3): 305-314 DOI:10.1007/s40304-013-0016-4