Applications of Nijenhuis Geometry V: Geodesic Equivalence and Finite-Dimensional Reductions of Integrable Quasilinear Systemsстатья
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Дата последнего поиска статьи во внешних источниках: 15 февраля 2024 г.
Аннотация:We describe all metrics geodesically compatible with a -regular Nijenhuis operator L. The set of such metrics is large enough so that a generic local curve is a geodesic for a suitable metric g from this set. Next, we show that a certain evolutionary PDE system of hydrodynamic type constructed from L preserves the property of to be a g-geodesic. This implies that every metric g geodesically compatible with L gives us a finite-dimensional reduction of this PDE system. We show that its restriction onto the set of g-geodesics is naturally equivalent to the Poisson action of on the cotangent bundle generated by the integrals coming from geodesic compatibility.