Journal of Convex Analysis 18 (2011), No. 2, 505--511
Copyright 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.
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