Abstract

Let K⊂R3K\subset \mathbb{R}^{3} be a convex body. A point p0p_{0} is a point of revolution for KK if every section of KK through p0p_{0} has an axis of symmetry that passes through p0p_{0}. In particular, every point that lies in an axis of revolution is a point of revolution. A line L⊂R3L\subset \mathbb{R}^3 is a false axis of revolution, if every point of LL is a point of revolution for KK but LL is not an axis of revolution. The purpose of this paper is to prove that only solid spheres admit a false axis of revolution

Author information

Contact details are reproduced from the original publication and may be historical.

Jesús Jerónimo-Castro

Dep. de Matemáticas UNAM, Circuito Ext. Cd. Universitaria, Colonia Copilco el Bajo, México D.F. - C.P. 04510
and: Facultad de Matemáticas, Universidad de Guerrero, México

jeronimo@cimat.mx

Luis Montejano

Instituto de Matemáticas UNAM, Circuito Ext. Cd. Universitaria, Colonia Copilco el Bajo, México D.F. - C.P. 04510
and: Centro de Innovacion Matemática, Queretaro, México

luis@matem.unam.mx

Efrén Morales-Amaya

Dep. de Matemáticas UNAM, Circuito Ext. Cd. Universitaria, Colonia Copilco el Bajo, México D.F. - C.P. 04510
and: Facultad de Matemáticas, Universidad de Guerrero, México

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Suggested citation

J. Jerónimo-Castro, L. Montejano, E. Morales-Amaya. “Only Solid Spheres Admit a False Axis of Revolution.” Journal of Convex Analysis 18 (2011), No. 2, 505–511. https://doi.org/10.68381/jca18032

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press LLC.