Further characterization of ellipsoids

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• 作者：Jesús Jerónimo-Castro (1) (2)
  
• 关键词：Ellipses ; Ellipsoids ; Convex bodies ; Affine normal vector ; Centroid ; Brunn’s theorem ; 52A10 ; 52A15
• 刊名：Monatshefte f眉r Mathematik
• 出版年：2010
• 出版时间：April 2010
• 年：2010
• 卷：160
• 期：1
• 页码：73-80
• 全文大小：175KB
• 参考文献：1. Blaschke W.: Vorlesungen üben Differentialgeometrie, II. Springer, Berlin (1923)
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• 作者单位：Jesús Jerónimo-Castro (1) (2)
  
  1. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Acapulco, Mexico
  2. Facultad de Matemáticas, Universidad Autónoma de Guerrero, Acapulco, Mexico
  
• ISSN：1436-5081

文摘

In this paper the following result is proved: Let K be a planar convex body and let γ be a differentiable closed convex curve. If for every point p in the interior of K the set of the midpoints, of all the chords through p, are forming a curve α(p) which is directly homothetic to γ, then K is an ellipse.