110 citations · 608 across the 39 of their papers we have counts for
23 papers · 1 filter
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…
On Separation of Variables for Symmetric Spaces of Rank1
Alexey Bolsinov, Holger R. Dullin, Vladimir. S. Matveev +1
We study existence and nonexistence of diagonal and separating coordinates for Riemannian symmetric spaces of rank 1. We generalize the results of Gauduchon and Moroianu, 2020, by…
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…
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…
Applications of Nijenhuis Geometry V: geodesically equivalent metrics and finite-dimensional reductions of certain integrable quasilinear systems
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We describe all metrics geodesically compatible with a gl-regular Nijenhuis operator . The set of such metrics is large enough so that a generic local curve is a geodesic fo…
Nijenhuis geometry IV: conservation laws, symmetries and integration of certain non-diagonalisable systems of hydrodynamic type in quadratures
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
The paper contains two lines of results: the first one is a study of symmetries and conservation laws of gl-regular Nijenhuis operators. We prove the splitting Theorem for symmetri…