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Mat. Sb., 2014, Volume 205, Number 7, Pages 25–42 (Mi msb8327)  

On the cylindricity of submanifolds containing a line in Minkowski space

A. A. Borisenko

Sumy State University

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.

DOI: https://doi.org/10.4213/sm8327

Full text: PDF file (507 kB)
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English version:
Sbornik: Mathematics, 2014, 205:7, 936–952

Bibliographic databases:

UDC: 514.774.2
MSC: 53A07, 53C21, 53C60
Received: 14.01.2014 and 01.04.2014

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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