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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: jeronimo@cimat.mx e-mail: luis@matem.unam.mx e-mail: efren@cimat.mx
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: jeronimo@cimat.mx e-mail: luis@matem.unam.mx e-mail: efren@cimat.mx
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: jeronimo@cimat.mx e-mail: luis@matem.unam.mx e-mail: efren@cimat.mx
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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

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