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Sbornik: Mathematics, 2014, Volume 205, Issue 7, Pages 936–952
DOI: https://doi.org/10.1070/SM2014v205n07ABEH004404 (Mi sm8327) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On the cylindricity of submanifolds containing a line in Minkowski space

A. A. Borisenko

Sumy State University
English version PDF (476 kB) Citations (1)
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DOI: https://doi.org/10.1070/SM2014v205n07ABEH004404
Abstract: We consider Finsler submanifolds in Minkowski spaces, and in particular, in Randers spaces. We give generalizations of the Toponogov and Cheeger-Gromoll theorems to the case of Randers spaces. Sufficient conditions are obtained for complete Finsler submanifolds in Minkowski spaces to be cylindrical. We also find conditions under which the convexity of a hypersurface in a Randers space implies that the flag curvature is positive.
Bibliography: 17 titles.
Keywords: flag curvature, Ricci curvature, Finsler metric, Riemannian metric, external zero-index, distribution.
Received: 14.01.2014 and 01.04.2014
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 7, Pages 25–42
DOI: https://doi.org/10.4213/sm8327
Bibliographic databases:
Document Type: Article
UDC: 514.774.2
MSC: 53A07, 53C21, 53C60
Language: English
Original paper language: Russian
Citation: A. A. Borisenko, “On the cylindricity of submanifolds containing a line in Minkowski space”, Mat. Sb., 205:7 (2014), 25–42; Sb. Math., 205:7 (2014), 936–952
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2014v205n07ABEH004404
  • https://www.mathnet.ru/eng/sm/v205/i7/p25
    • This publication is cited in the following 1 articles:
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    Abstract page:377
    Russian version PDF:164
    English version PDF:7
    References:42
    First page:31
     
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