arxiv_ready.pdf (411.73 kB)

Nijnehuis Geometry III: gl-regular Nijenhuis operators

Download (411.73 kB)
preprint
posted on 06.08.2020 by Alexey Bolsinov, Andrey Konyaev, Vladimir 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 describtion of such operators. We apply this local description to study singular points. In particular, we obtain their normal forms in dimension two and discover topological restrictions for the existence of gl-regular Nijenhuis operators on closed surfaces. This paper is an important step in the research programme suggested in arXiv:1903.04603 and arXiv:1903.06411.

History

School

  • Science

Department

  • Mathematical Sciences

Version

AO (Author's Original)

Rights holder

© The authors

Language

en

Depositor

Dr Alexey Bolsinov Deposit date: 3 August 2020

Exports

Logo branding

Categories

Exports