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Nijenhuis geometry III: gl-regular Nijenhuis operatorsстатья
Статья опубликована в высокорейтинговом журнале
Статья опубликована в журнале из списка Web of Science и/или Scopus- Авторы: Bolsinov Alexey V., Konyaev Andrey Yu, Matveev Vladimir S.
- Журнал: Revista Matematica Iberoamericana
- Год издания: 2023
- Издательство: Universidad Autonoma de Madrid
- Местоположение издательства: Spain
- DOI: 10.4171/rmi/1416
- Аннотация: 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.
- Добавил в систему: Коняев Андрей Юрьевич