Nijenhuis operators with a unity and F$F$‐manifolds

Авторы: Antonov Evgenii I., Konyaev Andrey Yu
Журнал: Journal of the London Mathematical Society
Том: 110
Номер: 3
Год издания: 2024
Издательство: Oxford University Press
Местоположение издательства: United Kingdom
DOI: 10.1112/jlms.12983
Аннотация: The core object of this paper is a pair (L, e), where L is a Nijenhuis operator and e is a vector field satisfying a specific Lie derivative condition, that is, e(L) = Id. Our research unfolds in two parts. In the first part, we establish a splitting theorem for Nijenhuis operators with a unity, offering an effective reduction of their study to cases where has either one real or two complex conjugate eigenvalues at a given point. We further provide the normal forms for gl-regular Nijenhuis operators with a unity around algebraically generic points, along with seminormal forms for dimensions 2 and 3. In the second part, we establish the relationship between Nijenhuis operators with a unity and F-manifolds. Specifically, we prove that the class of regular F-manifolds coincides with the class of Nijenhuis manifolds with a cyclic unity. Extending our results from dimension 3, we reveal seminormal forms for corresponding F-manifolds around singularities.
Добавил в систему: Коняев Андрей Юрьевич

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