Mokhov, O. I. Riemann invariants of semisimple non-locally bi-Hamiltonian systems of hydrodynamic type and compatible metrics. (English. Russian original) Zbl 1218.37092 Russ. Math. Surv. 65, No. 6, 1183-1185 (2010). In this paper, the non-singular non-locally bi-Hamiltonian system of hydrodynamic type is considered. For each such system, a full set of Riemann invariants that is completely determined by the metrics of the bi-Hamiltonian structure is constructed. The diagonalizability of all matrix differential-geometric objects associated with this system is proved. Reviewer: Vladislav Nikolaevich Dumachev (Voronezh) Cited in 4 Documents MSC: 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K25 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry 53B20 Local Riemannian geometry 70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics Keywords:bi-Hamiltonian system; non-local Poisson bracket of hydrodynamic type PDFBibTeX XMLCite \textit{O. I. Mokhov}, Russ. Math. Surv. 65, No. 6, 1183--1185 (2010; Zbl 1218.37092) Full Text: DOI