Geodesic
Dynamical and Topological Methods in Theory of Geodesically Equivalent Metrics
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 155-168

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We suggest a new, more global, approach to studying geodesically equivalent metrics, which is based on applying the theory of integrable geodesic flows. 
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     title = {Dynamical and {Topological} {Methods} in {Theory} of {Geodesically} {Equivalent} {Metrics}},
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V. S. Matveev; P. J. Topalov. Dynamical and Topological Methods in Theory of Geodesically Equivalent Metrics. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 155-168. http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a9/