Journal of Convex Analysis 24 (2017), No. 2, 685--693
Copyright Heldermann Verlag 2017
Convex Bodies with Many Elliptic Sections
Isaac Arelio
Instituto de Matemáticas UNAM, Circuito Ext. Cd. Universitaria, Colonia Copilco el Bajo, México D.F. - C.P. 04510
incordio@im.unam.mx
Luis Montejano
Instituto de Matemáticas UNAM, Circuito Ext. Cd. Universitaria, Colonia Copilco el Bajo, México D.F. - C.P. 04510
luis@matem.unam.mx
We show in this paper that two normal elliptic sections through every point of the boundary of a smooth convex body essentially characterize an ellipsoid and furthermore, that four different pairwise non-tangent elliptic sections through every point of the C2-differentiable boundary of a convex body also essentially characterize an ellipsoid.
Keywords: Convex surface, quadric surface, quadric curve,planar section, characterization of ellipsoid.
MSC: 52A15, 53A04, 53A05
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