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This article is cited in 1 scientific paper (total in 1 paper)
Polar transform of conformally flat metrics
E. D. Rodionova, V. V. Slavskiĭb a Altai State University, Barnaul, Russia
b Yugra State University, Khanty-Mansiysk, Russia
Abstract:
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.
Key words:
Lobachevskiĭ geometry, convex set, conformally flat metric.
Received: 01.10.2016
Citation:
E. D. Rodionov, V. V. Slavskiǐ, “Polar transform of conformally flat metrics”, Mat. Tr., 20:2 (2017), 120–138; Siberian Adv. Math., 28:2 (2018), 101–114
Linking options:
https://www.mathnet.ru/eng/mt326 https://www.mathnet.ru/eng/mt/v20/i2/p120
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Abstract page: | 248 | Full-text PDF : | 105 | References: | 36 | First page: | 10 |
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