Nijenhuis geometry III: gl-regular Nijenhuis operators

Alexey V. Bolsinov ^[1] ; Andrey Yu. Konyaev ^[2] ; Vladimir S. Matveev ^[3]
1. [1] Loughborough University
  
  Loughborough University
  
  Charnwood District, Reino Unido
2. [2] Moscow State University
  
  Moscow State University
  
  Rusia
3. [3] Friedrich Schiller Universität Jena, Germany
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Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 1, 2024, págs. 155-188
Idioma: inglés
DOI: 10.4171/RMI/1416
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Resumen
- 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.