Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 18 (2011), No. 2, 505--511Copyright Heldermann Verlag 2011 Only Solid Spheres Admit a False Axis of Revolution Jesus 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 [Abstract-pdf] Let $K\subset \mathbb{R}^{3}$ be a convex body. A point $p_{0}$ is a point of revolution for $K$ if every section of $K$ through $p_{0}$ has an axis of symmetry that passes through $p_{0}$. In particular, every point that lies in an axis of revolution is a point of revolution. A line $L\subset \mathbb{R}^3$ is a \textit{false axis of revolution}, if every point of $L$ is a point of revolution for $K$ but $L$ is not an axis of revolution. The purpose of this paper is to prove that only solid spheres admit a false axis of revolution. [ Fulltext-pdf  (98  KB)] for subscribers only.