Nijnehuis Geometry III: gl-regular Nijenhuis operators
Differential Geometry
2023-04-28 v1 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.2007.09506,
title = {Nijnehuis Geometry III: gl-regular Nijenhuis operators},
author = {Alexey Bolsinov and Andrey Konyaev and Vladimir Matveev},
journal= {arXiv preprint arXiv:2007.09506},
year = {2023}
}