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Integrability of generalized pluriharmonic maps

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In this paper we provide examples of maps from almost complex domains into pseudo-Riemannian symmetric targets, which are pluriharmonic and not integrable, i.e. do not admit an associated family. More precisely, for one class of examples the source has a non-integrable complex structure, like for instance a nearly Kähler structure and the target is a Riemannian symmetric space and for the other class the source is a complex manifold and the target is a pseudo-Riemannian symmetric space. These examples show, that a former result, Theorem 5.3 of [12], on the existence of associated families is sharp.

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  1. Institut für Differentialgeometrie, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    Lars Schäfer

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Schäfer, L. Integrability of generalized pluriharmonic maps. manuscripta math. 146, 473–493 (2015). https://doi.org/10.1007/s00229-014-0714-6

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