Hierarchy of integrable geodesic flows
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A family of integrable geodesic flows is obtained. Any such a family corresponds to a pair of geodesically equivalent metrics.
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Topalov, P. «Hierarchy of integrable geodesic flows». Publicacions Matemàtiques, 2000, vol.VOL 44, núm. 1, p. 257-76, https://raco.cat/index.php/PublicacionsMatematiques/article/view/37984.