6 papers · 1 filter
Local description of gl-regular Haantjes operators
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We study Haantjes operators, that is, (1,1)-tensor fields with vanishing Haantjes torsion. Our main result is a complete local description of gl-regular Haantjes operators. Additio…
Duality of operator Frobenius algebras and solution of Eisenhart-Stäckel problem in the non-diagonal case
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We study Frobenius algebras of operator fields and introduce a novel notion of duality for them. We show that, under the assumption that the operator fields forming the Frobenius a…
On the Linearization of Certain Singularities of Nijenhuis Operators
Andrey Yu. Konyaev
We consider a linearization problem for Nijenhuis operators in dimension two around a point of scalar type in analytic category. The problem was almost completely solved in arXiv:1…
On the Jordan-Chevalley decomposition problem for operator fields in small dimensions and Tempesta-Tondo conjecture
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We explore the Jordan-Chevalley decomposition problem for an operator field in small dimensions. In dimensions three and four, we find tensorial conditions for an operator field $L…
Integrability of the magnetic geodesic flow on the sphere with a constant 2-form
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We prove a recent conjecture of Dragovic et al arXiv2504.20515 stating that the magnetic geodesic flow on the standard sphere whose magnetic 2-form is…
Research problems on relations between Nijenhuis geometry and integrable systems
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
The paper surveys open problems and questions related to interplay between the theory of integrable systems with infinitely and finitely many degrees of freedom and Nijenhuis geome…