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  • 1 Universidad Autónoma de Querétaro, Centro Universitario, Cerro de las Campanas s/n C.P. 76010, Santiago de Querétaro, Qro., MEXICO
  • | 2 Alfréd Rényi Mathematical Institute, Hungarian Academy of Sciences, H-1364 Budapest, Pf. 127, HUNGARY
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High proved the following theorem. If the intersections of any two congruent copies of a plane convex body are centrally symmetric, then this body is a circle. In our paper we extend the theorem of High to spherical, Euclidean and hyperbolic spaces, under some regularity assumptions. Suppose that in any of these spaces there is a pair of closed convex sets of class C+2 with interior points, different from the whole space, and the intersections of any congruent copies of these sets are centrally symmetric (provided they have non-empty interiors). Then our sets are congruent balls. Under the same hypotheses, but if we require only central symmetry of small intersections, then our sets are either congruent balls, or paraballs, or have as connected components of their boundaries congruent hyperspheres (and the converse implication also holds).

Under the same hypotheses, if we require central symmetry of all compact intersections, then either our sets are congruent balls or paraballs, or have as connected components of their boundaries congruent hyperspheres, and either d ≥ 3, or d = 2 and one of the sets is bounded by one hypercycle, or both sets are congruent parallel domains of straight lines, or there are no more compact intersections than those bounded by two finite hypercycle arcs (and the converse implication also holds).

We also prove a dual theorem. If in any of these spaces there is a pair of smooth closed convex sets, such that both of them have supporting spheres at any of their boundary points Sd for Sd of radius less than π/2- and the closed convex hulls of any congruent copies of these sets are centrally symmetric, then our sets are congruent balls.

  • [1]

    Alekseevskij, D. V., Vinberg, E. B. and Solodovnikov, A. S.. Geometry of spaces of constant curvature, Geometry II (Ed. E. B. Vinberg), Enc. Math. Sci. 29, 1138, Springer, Berlin, 1993, MR 95b:53042.

    • Search Google Scholar
    • Export Citation
  • [2]

    Baldus, R., Nichteuklidische Geometrie. Hyperbolische Geometrie der Ebene, 4-te Au. Bearb. und ergánzt von F. Löbell, Sammlung Göschen 970/970a, de Gruyter, Berlin, 1964, MR 29#3936.

    • Search Google Scholar
    • Export Citation
  • [3]

    Bonnesen, T. and Fenchel, W., Theorie der konvexen Körper, Berichtigter Reprint, Springer, Berlin-New York, 1974. English transl.: Theory of convex bodies, Translated from the German and edited by L. Boron, C. Christenson, B. Schmidt, BCS Associates, Moscow, ID, 1987, MR 49#9736, 88j:52001.

    • Search Google Scholar
    • Export Citation
  • [4]

    Bonola, R., Non-Euclidean geometry, a critical and historical study of its developments, With a Supplement containing the G. B. Halstead translations of "The science of absolute space" by, J. Bolyai and "The theory of parallels" by N. Lobachevski, Dover Publs. Inc., New York, N.Y., 1955, MR 16-1145.

    • Search Google Scholar
    • Export Citation
  • [5]

    Coxeter, H. S. M., Non-Euclidean Geometry, 6-th ed., Spectrum Series, The Math. Ass. of America, Washington, DC, 1998, MR 99c:51002.

  • [6]

    Heil, E. and Martini, H., Special convex bodies, in: Handbook of Convex Geometry, (eds. P. M. Gruber, J. M. Wills), North-Holland, Amsterdam etc., 1993, Ch. 1.11, 347385, MR 94h:52001.

    • Search Google Scholar
    • Export Citation
  • [7]

    High, R., Characterization of a disc, Solution to problem 1360 (posed by P. R. Scott), Math. Magazine 64 (1991), 353354.

  • [8]

    Liebmann, H., Nichteuklidische Geometrie, 3-te Au age, de Gruyter, Berlin, 1923, Jahrbuch Fortschr. Math. 49, 390.

  • [9]

    Perron, O., Nichteuklidische Elementargeometrie der Ebene, Math. Leitfáden Teubner, Stuttgart, 1962, MR 25#2489.

  • [10]

    Schneider, R., Convex bodies: the Brunn-Minkowski theory, Encyclopedia of Math. and its Appl., 44, Cambridge Univ. Press, Cambridge, 1993. Second expanded ed., Encyclopaedia of Math. and its Appl., 151, Cambridge Univ. Press, Cambridge, 2014 MR 94d:52007, 3155183

    • Search Google Scholar
    • Export Citation
  • [11]

    Soltan, V., Pairs of convex bodies with centrally symmetric intersections of translates, Discr. Comput. Geom. 33 (2005), 605616, MR 2005k:52012.

    • Search Google Scholar
    • Export Citation
  • [12]

    Soltan, V., Line-free convex bodies with centrally symmetric intersections of translates, Revue Roumaine Math. Pures Appl. 51 (2006), 111123, MR 2007k:52010. Also in: Papers on Convexity and Discrete Geometry, Ded. to T. Zamfirescu on the occasion of his 60-th birthday, Editura Acad. Romane, Bucureâsti, 2006, 411–423.

    • Search Google Scholar
    • Export Citation
  • [13]

    Stoker, J. J., Differential Geometry, New York Univ., Inst. Math. Sci. New York, 1956.

  • [14]

    Vermes, I., Über die synthetische Behandlung der Krümmung und des Schmiegzykels der ebenen Kurven in der, Bolyai-Lobatschefskyschen Geometrie, Stud. Sci. Math. Hungar., 28 (1993), 289297. MR 95e:51030.

    • Search Google Scholar
    • Export Citation

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

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Total Cites 536
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2019  
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WoS
463
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without
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0,468
5 Year
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37
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Studia Scientiarum Mathematicarum Hungarica
Language English
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2021 Volume 58
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ISSN 0081-6906 (Print)
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