On Characterizations of Some General $(\alpha, \beta)$ Norms in a Minkowski Space

Yan Li

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arXiv · 1505.00554

On Characterizations of Some General $(\alpha, \beta)$ Norms in a Minkowski Space

Yan Li

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Abstract

General $(\alpha, \beta)$ norms are an important class of Minkowski norms which contains the original $(\alpha, \beta)$ norms. In this note, by studying the behavior of the Darboux curves of the indicatrix, we give a characterization of 3-dimensional general $(\alpha, \beta)$ norms. By studying the isoperimetric properties of the indicatrix, as well as the isoperimetric inequalities in a Minkowski space, we give some global geometric quantities which characterizes Randers norms of arbitrary dimensions.

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Yan Li. 2015-05-04. On Characterizations of Some General $(\alpha, \beta)$ Norms in a Minkowski Space. https://arxiv.org/abs/1505.00554

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