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Nijenhuis geometry III: gl-regular Nijenhuis operators

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posted on 2023-03-07, 11:37 authored by Alexey BolsinovAlexey Bolsinov, Andrey Yu Konyaev, Vladimir S Matveev

We study Nijenhuis operators, that is, (1,1)-tensors with vanishing Nijenhuis torsion under the additional assumption that they are gl-regular, i.e., every eigenvalue has geometric multiplicity one. We prove the existence of a coordinate system in which the operator takes first or second companion form, and give a local description of such operators. We apply this local description to study singular points. In particular, we obtain normal forms of gl-regular Nijenhuis operators near singular points in dimension two and discover topological restrictions for the existence of gl-regular Nijenhuis operators on closed surfaces.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Revista Matemática Iberoamericana

Publisher

EMS Press

Version

  • AM (Accepted Manuscript)

Rights holder

© EMS Press

Publisher statement

This paper was accepted for publication in the journal Revista Matemática Iberoamericana and the definitive published version is available at https://doi.org/10.4171/rmi/1416

Acceptance date

2023-01-17

Publication date

2023-03-03

Copyright date

2023

ISSN

0213-2230

eISSN

2235-0616

Language

  • en

Depositor

Dr Alexey Bolsinov. Deposit date: 6 March 2023

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