Geodesic
Only Solid Spheres Admit a False Axis of Revolution
Journal of convex analysis, Tome 18 (2011) no. 2, pp. 505-511
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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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     author = {J. Jer\'onimo-Castro and L. Montejano and E. Morales-Amaya},
     title = {Only {Solid} {Spheres} {Admit} a {False} {Axis} of {Revolution}},
     journal = {Journal of convex analysis},
     pages = {505--511},
     year = {2011},
     volume = {18},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_2_JCA_2011_18_2_a15/}
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J. Jerónimo-Castro; L. Montejano; E. Morales-Amaya. Only Solid Spheres Admit a False Axis of Revolution. Journal of convex analysis, Tome 18 (2011) no. 2, pp. 505-511. http://geodesic.mathdoc.fr/item/JCA_2011_18_2_JCA_2011_18_2_a15/