14 papers
Quadratic Killing tensors on classical Lie groups are decomposable
Vladimir Matveev, An Ky Nguyen, Yuri Nikolayevsky
A Killing tensor field on a Riemannian manifold is a covariant symmetric tensor field whose contraction with the velocity vector along a geodesic produces a homogeneous pol…
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…
On Killing tensors on Riemannian symmetric spaces
Vladimir Matveev, Yuri Nikolayevsky
A Killing tensor field on a Riemannian space corresponds to an integral of the geodesic flow polynomial in momenta. A Killing tensor field is called decomposable if it is a polynom…
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…
Existence of Riemannian invariants for integrable systems of hydrodynamic type
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We show that for a hyperbolic system of hydrodynamic type admitting n symmetries, there exists a coordinate system in which the generator of the system and all the symmetries are d…
Lax pairs for BKM hierarchy
Andrey Yu. Konyaev, Vladimir S. Matveev
We construct Lax pairs for the recently (2023) introduced integrable PDE systems known as the BKM equations. As many known and previously studied integrable systems are special cas…