Geodesic
A metric on a sphere that is geodesically equivalent to itself a metric of constant curvature is a metric of constant curvature
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (1998), pp. 53-55
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     author = {V. S. Matveev and P. Topalov},
     title = {A metric on a sphere that is geodesically equivalent to itself a metric of constant curvature is a metric of constant curvature},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {53--55},
     year = {1998},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1998_5_a10/}
}
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V. S. Matveev; P. Topalov. A metric on a sphere that is geodesically equivalent to itself a metric of constant curvature is a metric of constant curvature. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (1998), pp. 53-55. http://geodesic.mathdoc.fr/item/VMUMM_1998_5_a10/