Abstract
As it is well-known a Minkowski space is a finite dimensional real vector space equipped with a Minkowski functional F. If the square of the Minkowski functional is quadratic then we have an Euclidean space and the indicatrix hypersurface S:= F-1 (1) has constant 1 curvature. In his classical paper [1] F. Brickell proved that the converse is also true provided that the indicatrix is symmetric with respect to the origin. M. Ji and Z. Shen investigated the (sectional) curvature of Randers indicatrices and it always turned out greater than zero and less or equal than 1; see [3]. In this note we give a general lower and upper bound for the curvature in terms of the norm of the Cartan tensor.
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References
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Supported by FKFP (0184/2001), Hungary.
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Vincze, C. On the Curvature of the Indicatrix Surface in Three-Dimensional Minkowski Spaces. Periodica Mathematica Hungarica 48, 69–76 (2004). https://doi.org/10.1007/BF03379747
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DOI: https://doi.org/10.1007/BF03379747