ON ORTHOGONAL CHORDS IN NORMED PLANES

被引：3

作者：

Alonso, Javier ^{[1
]}

Martini, Horst ^{[2
]}

Mustafaev, Zokhrab ^{[3
]}

机构：

[1] Univ Extremadura, Dept Math, Badajoz 06006, Spain

[2] Univ Technol Chemnitz, Fac Math, D-09107 Chemnitz, Germany

[3] Univ Houston Clear Lake City, Dept Math, Houston, TX 77058 USA

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2011年 / 41卷 / 01期

关键词：

Birkhoff orthogonality; convex figure; constant width; isosceles orthogonality; maximal chord; normed plane;

D O I：

10.1216/RMJ-2011-41-1-23

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is known that a convex plate of diameter I in the Euclidean plane is of constant width 1 if and only if any two perpendicular intersecting chords have total length at least 1. We show that, in general, this result cannot be extended to normed (or Minkowski) planes when the type of orthogonality is defined in the sense of Birkhoff. Inspired by this, we present also further results on intersecting chords in normed planes that are orthogonal in the sense of Birkhoff and in the sense of James.

引用

页码：23 / 35

页数：13

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