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Matematicheskie Trudy, 2017, Volume 20, Number 2, Pages 120–138
DOI: https://doi.org/10.17377/mattrudy.2017.20.206 (Mi mt326) 		 
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
Full-text PDF (370 kB) Citations (1)
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DOI: https://doi.org/10.17377/mattrudy.2017.20.206
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.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1148
Russian Foundation for Basic Research 15-41-00092-r-Urals
15-41-00063-r-Urals
15-01-06582-a
16-01-00336-a
Received: 01.10.2016
English version:
Siberian Advances in Mathematics, 2018, Volume 28, Issue 2, Pages 101–114
DOI: https://doi.org/10.3103/S1055134418020025
Bibliographic databases:
Document Type: Article
UDC: 514.7
Language: Russian
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
Citation in format AMSBIB
\Bibitem{RodSla17}
\by E.~D.~Rodionov, V.~V.~Slavski{\v\i}
\paper Polar transform of conformally flat metrics
\jour Mat. Tr.
\yr 2017
\vol 20
\issue 2
\pages 120--138
\mathnet{http://mi.mathnet.ru/mt326}
\crossref{https://doi.org/10.17377/mattrudy.2017.20.206}
\elib{https://elibrary.ru/item.asp?id=30558047}
\transl
\jour Siberian Adv. Math.
\yr 2018
\vol 28
\issue 2
\pages 101--114
\crossref{https://doi.org/10.3103/S1055134418020025}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85047985057}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические труды Siberian Advances in Mathematics
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    Full-text PDF :105
    References:36
    First page:10
     
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