Characterization of different classes of convex bodies via orthogonality
Javier Alonso and Margarita Spirova
Source: Bull. Belg. Math. Soc. Simon Stevin Volume 18, Number 4
(2011), 707-721.
Abstract
Following the concept of normal to a convex body, which is due to Eggleston, we introduce the notion of affine orthogonality with respect to a convex body. In contrast to Eggleston's considerations, we do not need a metric and via this notion we are able to characterize convex bodies of constant width and further interesting classes of convex bodies.
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Keywords: Affine diameter; convex bodies of constant width; centrally symmetric convex bodies; finite-dimensional Banach spaces; Minkowski geometry; normal to a convex body; normed spaces
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Bulletin of the Belgian Mathematical Society - Simon Stevin
