On Characterizations of Some General (α, β) Norms in a Minkowski Space

2015/05/04 by Yan Li, Li, Yan
Mathematics · #53A15 #53C60 #54C45 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A15 #msc:53C60 #msc:54C45

paper · pdf · doi:10.48550/arxiv.1505.00554

arxiv created 2015/05/04 · arxiv updated 2015/05/05

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.

Related

• An equivalence theorem of a class of Minkowski norms and its applications
• Deforming convex bodies in Minkowski geometry
• π_B in asymetric Minkowski normed spaces
• An Isoperimetric-Type Inequality for Spacelike Submanifold in the Minkowski Space
• Angle measures, general rotations, and roulettes in normed planes