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Some characterizations of conics and hypersurfaces with centrally symmetric hyperplane sections

김동수|김원용|방신옥|김동서
대한수학회 (The Korean Mathematical Society)|2024.01|대한수학회논문집 (Communications of the KMS)|제39권 제1호|pp. 211-221|DOI 10.4134/CKMS.c230119

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키워드

ellipsoidConicelliptic paraboloidelliptic hyperboloid
주제분류수학

초록

Parallel conics have interesting area and chord properties. In this paper, we study such properties of conics and conic hypersurfaces. First of all, we characterize conics in the plane with respect to the above mentioned properties. Finally, we establish some characterizations of hypersurfaces with centrally symmetric hyperplane sections.

Abstract

Parallel conics have interesting area and chord properties. In this paper, we study such properties of conics and conic hypersurfaces. First of all, we characterize conics in the plane with respect to the above mentioned properties. Finally, we establish some characterizations of hypersurfaces with centrally symmetric hyperplane sections.

참고문헌 (17)

  1. ´A. B´enyi, "Archimedean properties of parabolas", Amer. Math. Monthly, 107(10), pp.945~949 (2000)[DOI]
  2. ´A. B´enyi, "A generalized Archimedean property", Real Anal. Exchange, 29(2), pp.881~889 (2003)
  3. ´ O. Ciaurri, "Revisiting floating bodies", Expo. Math, 34(4), pp.396~422 (2016)[DOI]
  4. D. -S. Kim, "Ellipsoids and elliptic hyperboloids in the Euclidean space En+1", Linear Algebra Appl, 471, pp.28~45 (2015)[DOI]
  5. D. -S. Kim, "A characterization of conic sections", Honam Math. J, 33(3), pp.335~340 (2011)[DOI]
  6. D. -S. Kim, "A characterization of ellipses", Amer. Math. Monthly, 114(1), pp.66~70 (2007)[DOI]
  7. D. -S. Kim, "New characterizations of spheres, cylinders and W-curves", Linear Algebra Appl, 432(11), pp.3002~3006 (2010)[DOI]
  8. D. -S. Kim, "Some characterizations of spheres and elliptic paraboloids", Linear Algebra Appl, 437(1), pp.113~120 (2012)[DOI]
  9. D. -S. Kim, "Some characterizations of spheres and elliptic paraboloids II", Linear Algebra Appl, 438(3), pp.1356~1364 (2013)[DOI]
  10. D. -S. Kim, "On the Archimedean characterization of parabolas", Bull. Korean Math. Soc, 50(6), pp.2103~2114 (2013)[DOI]
  11. D. -S. Kim, "A characterization of concentric hyperspheres in Rn", Bull. Korean Math. Soc, 51(2), pp.531~538 (2014)[DOI]
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  13. D. -S. Kim, "Center of gravity and a characterization of parabolas", Kyungpook Math. J, 55(2), pp.473~484 (2015)[DOI]
  14. D. -S. Kim, "Area of triangles associated with a curve", Bull. Korean Math. Soc, 51(3), pp.901~909 (2014)[DOI]
  15. D. -S. Kim, "A characterization of elliptic hyperboloids", Honam Math. J, 35(1), pp.37~49 (2013)[DOI]
  16. J. Krawczyk, "On areas associated with a curve", Zesz. Nauk. Uniw. Opol. Mat, 29, pp.97~101 (1995)
  17. B. Richmond, "How to recognize a parabola", Amer. Math. Monthly, 116(10), pp.910~922 (2009)[DOI]

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