5 papers
Beltrami problem in dimension two: local normal forms
Dinmukhammed Akpan, Alexey Bolsinov
Two (pseudo-)Riemannian metrics are said to be geodesically equivalent if they share the same geodesics considered as unparametrized curves. In 1865, E. Beltrami posed the problem…
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…
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…
Jordan-Kronecker invariants of Lie algebra representations and degrees of invariant polynomials
Alexey Bolsinov, Anton Izosimov, Ivan Kozlov
For an arbitrary representation of a complex finite-dimensional Lie algebra, we construct a collection of numbers that we call the Jordan-Kronecker invariants of . Among oth…