On Characterizations of Some General (α, β) Norms in a Minkowski Space
Abstract
General (α, β) norms are an important class of Minkowski norms which contains the original (α, β) norms. In this note, by studying the behavior of the Darboux curves of the indicatrix, we give a characterization of 3-dimensional general (α, β) 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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