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Shaken Rogers's Theorem for Homothetic Sections

Published online by Cambridge University Press:  20 November 2018

J. Jerónimo-Castro ,
L. Montejano  and
E. Morales-Amaya
J. Jerónimo-Castro
Affiliation:
Instituto de Matemáticas, UNAM, Ciudad Universitaria, C.P. 04510, México, D.F., andFacultad de Matemáticas, Acapulco, Universidad Autónoma de Guerrero e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]
L. Montejano
Affiliation:
Instituto de Matemáticas, UNAM, Ciudad Universitaria, C.P. 04510, México, D.F., andFacultad de Matemáticas, Acapulco, Universidad Autónoma de Guerrero e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]
E. Morales-Amaya
Affiliation:
Instituto de Matemáticas, UNAM, Ciudad Universitaria, C.P. 04510, México, D.F., andFacultad de Matemáticas, Acapulco, Universidad Autónoma de Guerrero e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]
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Abstract

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We shall prove the following shaken Rogers's theorem for homothetic sections: Let $K$ and $L$ be strictly convex bodies and suppose that for every plane $H$ through the origin we can choose continuously sections of $K$ and $L$, parallel to $H$, which are directly homothetic. Then $K$ and $L$ are directly homothetic.

Keywords

52A15convex bodieshomothetic bodiessections and projectionsRogers's Theorem
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 3 , 01 September 2009 , pp. 403 - 406
Copyright
Copyright © Canadian Mathematical Society 2009

References

[1] Aitchison, P. W., Petty, C. M., and Rogers, C. A., A convex body with a false centre is an ellipsoid. Mathematika 18(1971), 50–59.Google Scholar
[2] Larman, D. G., A note in the false centre theorem. Mathematika 21(1974), 216–227.Google Scholar
[3] Montejano, L., Convex bodies with homothetic sections. Bull. London Math. Soc. 23(1991), no. 4, 381–386.Google Scholar
[4] Montejano, L., Two applications of topology to convex geometry. Proc. Steklov Inst. Math. 247(2004), 164–167.Google Scholar
[5] Montejano, L. and Morales, E., Variations of classic characterizations of ellipsoids and a short proof of the false centre theorem. Mathematika 54(2007), no. 1-2, 35–40.Google Scholar
[6] Rogers, C. A., Sections and projections of convex bodies. Portugal Math. 24(1965), 99–103.Google Scholar
[7] Steenrod, N. E. and Epstein, D. B. A., Cohomology Operations. Princeton University Press, 1962.Google Scholar