Nijenhuis geometry III: gl-regular Nijenhuis operators
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.
- Mathematical Sciences
Published inRevista Matemática Iberoamericana
- AM (Accepted Manuscript)
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Publisher statementThis 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