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arXiv · 2606.04985

Local description of gl-regular Haantjes operators

Alexey V. Bolsinov·Andrey Yu. Konyaev·Vladimir S. Matveev
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Abstract

We study Haantjes operators, that is, (1,1)-tensor fields with vanishing Haantjes torsion. Our main result is a complete local description of gl-regular Haantjes operators. Additional results include a splitting theorem for general (not necessarily gl-regular) Haantjes operators and, more generally, for operators with vanishing generalised Nijenhuis torsion of an arbitrary level, as well as a complete treatment and understanding of the case when the eigenvalues of a Haantjes operator are complex; the latter case was ignored in many previous papers on this and related topics.

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BibTeXRIS

Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev. 2026-06-03. Local description of gl-regular Haantjes operators. https://arxiv.org/abs/2606.04985

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