## Convex bodies with many elliptic sections

*Arelio, Isaac*;

*Montejano, Luis*;

- Subject: Mathematics - Metric Geometry | 52A15, 53A04, 53A05

- References (9)
[1] Alonso, J. and Mart n, P. Some characterizations of ellipsoids by sections, Discrete and Computational Geometry, Vol. 31, 2004, pp. 643{654.

[2] Bianchi, G. and Gruber P. M. Characterizations of ellipsoids, Arch. Math. Vol. 49, 1987, pp. 344{350. Verlag, 2008.

[3] Hammer, P. C. Diameters of convex bodies, Proc. Amer. Math. Soc. 5, 1954, pp. 304{306.

[4] Makeev, V. V. A ne diameters and chords of convex compacta, Journal of Mathematical Sciences, Vol. 131, No. 1, 2005, pp. 5401{5405.

[5] Miyaoka R. and Takeuchi N. A note on Ogiue-Takagi conjecture on a characterization of euclidean 2-spheres, Memoirs of the Faculty of Science, Kyushu University Ser. A, Vol. 46, No. 1, 1992, pp. 129{135.

[6] Montejano, L. Cuerpos de ancho constante, Ediciones Cient cas Universitarias. Fondo de Cultura Economica, 1a Edicion, 1998.

[7] Sobczyk, A. Simple families of lines, Paci c J. Math. Vol. 6, Num. 3, 1956, pp. 541{552.

[8] Stein, S. Families of curves, Proc. Amer. Math. Soc., Vol. 5, Num. 5, 1954, pp. 745{747.

[9] Takeuchi N. A sphere as a surface which contains many circles II, Journal of Geometry Vol. 34, 1989, pp. 195{200.

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