Polar Transform of Conformally Flat Metrics

Polar Transform of Conformally Flat Metrics

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 iso...

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Veröffentlicht in:Siberian advances in mathematics 2018-04, Vol.28 (2), p.101-114
Hauptverfasser: Rodionov, E. D., Slavskiĭ, V. V.
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Euclidean geometry
Euclidean space
Mathematics
Mathematics and Statistics
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Slavskiĭ, V. V.
description 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.
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subjects Euclidean geometry
Euclidean space
Mathematics
Mathematics and Statistics
title Polar Transform of Conformally Flat Metrics
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