This article is cited in 1 paper

Polar transform of conformally flat metrics

E. D. Rodionov^a, V. V. Slavskiĭ<sup>b

a</sup> 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.

UDC: 514.7

Received: 01.10.2016

DOI: 10.17377/mattrudy.2017.20.206

 English version: Siberian Advances in Mathematics, 2018, 28:2, 101–114

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