Geodesic
Polar transform of conformally flat metrics
Matematičeskie trudy, Tome 20 (2017) no. 2, pp. 120-138

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In the theory of convex subsets in a Euclidean space, an important role is played by Minkowski duality (the polar transform of a convex set, or the Legendre transform of a convex set). We consider conformally flat Riemannian metrics on the $n$-dimensional unit sphere and their embeddings into the isotropic cone of the Lorentz space. For a given class of metrics, we define and carry out a detailed study of the Legendre transform. 
@article{MT_2017_20_2_a5,
     author = {E. D. Rodionov and V. V. Slavskiǐ},
     title = {Polar transform of conformally flat metrics},
     journal = {Matemati\v{c}eskie trudy},
     pages = {120--138},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2017_20_2_a5/}
}
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E. D. Rodionov; V. V. Slavskiǐ. Polar transform of conformally flat metrics. Matematičeskie trudy, Tome 20 (2017) no. 2, pp. 120-138. http://geodesic.mathdoc.fr/item/MT_2017_20_2_a5/