78 citations · 1.2k across the 112 of their papers we have counts for
117 papers
Rotationally Symmetric Zoll Metrics with a Cubic Integral
Holger R. Dullin, Vladimir S. Matveev, Gleb P. Palshin +1
We introduce a new method for constructing Zoll metrics that admit first integrals polynomial in the momenta. The method uses Funk's form of the metric together with an algebraic r…
Sophus Lie's problem on two-dimensional metrics with projective symmetries: completing the local classification
Gianni Manno, Vladimir S. Matveev, Filippo Salis
We complete the local classification, up to isometry, of -dimensional pseudo-Riemannian metrics (i.e. both Riemannian and Lorentzian), admitting a projective symmetry algebra of…
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…