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.
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