Geodesic
Generalized Legendre transform of conformally flat metrics
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 4, Tome 182 (2020), pp. 55-65.

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In the calculus of variations, an important role is played by the Minkowski duality, or the Legendre transform of convex functions. We consider weakly regular, conformally flat Riemannian metrics of nonnegative curvature defined on the $n$-dimensional unit sphere. For this class of metrics, an analog of the Legendre transformation is introduced and studied in detail.
Mots-clés : Legendre transform
Keywords: conformally flat metric, Lobachevsky space. 
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M. V. Kurkina; E. D. Rodionov; S. P. Semenov; V. V. Slavskii. Generalized Legendre transform of conformally flat metrics. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 4, Tome 182 (2020), pp. 55-65. http://geodesic.mathdoc.fr/item/INTO_2020_182_a9/

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