Hyperbolic is the only Hilbert geometry having circumcenter or orthocenter generally

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• 作者：József Kozma ; Árpád Kurusa
• 关键词：Hilbert geometry ; Hyperbolic geometry ; Circumcenter ; Orthocenter ; Ellipsoid characterization ; 53A35 ; 51M09 ; 52A20
• 刊名：Beitr?ge zur Algebra und Geometrie / Contributions to Algebra and Geometry
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：57
• 期：1
• 页码：243-258
• 全文大小：833 KB
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• 作者单位：József Kozma (1)
  Árpád Kurusa (1)
  
  1. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6725, Szeged, Hungary
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra
  Convex and Discrete Geometry
  Geometry
  Algebraic Geometry
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2191-0383

文摘

A Hilbert geometry is hyperbolic if and only if the perpendicular bisectors or the altitudes of any trigon form a pencil. We also prove some interesting characterizations of the ellipse. Keywords Hilbert geometry Hyperbolic geometry Circumcenter Orthocenter Ellipsoid characterization