22 citations · 70 across the 13 of their papers we have counts for
12 papers · 1 filter
Webs, Nijenhuis operators, and heavenly PDEs
Andriy Panasyuk, Adam Szereszewski
In 1989 Mason and Newman proved that there is a 1-1-correspondence between self-dual metrics satisfying Einstein vacuum equation (in complex case or in neutral signature) and pairs…
On linear-quadratic Poisson pencils on trivial central extensions of semisimple Lie algebras
Andriy Panasyuk, Vsevolod Shevchishin
The paper is devoted to quadratic Poisson structures compatible with the canonical linear Poisson structures on trivial 1-dimensional central extensions of semisimple Lie algebras.…
Invariant Nijenhuis Tensors and Integrable Geodesic Flows
Konrad Lompert, Andriy Panasyuk
We study invariant Nijenhuis -tensors on a homogeneous space of a reductive Lie group from the point of view of integrability of a Hamiltonian system of differenti…
Kronecker webs, Nijenhuis operators, and nonlinear PDEs
Andriy Panasyuk
The aim of this paper is two-fold. First, a survey of the theory of Kronecker webs and their relations with bihamiltonian structures and PDEs is presented. Second, a partial soluti…
Dirac brackets and reduction of invariant bi-Poisson structures
Ihor V. Mykytyuk, Andriy Panasyuk
Let be a manifold with a bi-Poisson structure generated by a pair of -invariant symplectic structures and , where the Lie group acts properly on …
Veronese webs and nonlinear PDEs
Boris Kruglikov, Andriy Panasyuk
Veronese webs are closely related to bi-Hamiltonian systems, as was shown by Gelfand and Zakharevich. Recently a correspondence between Veronese three-dimensional webs and three-di…