Geodesic
Convex Bodies with Many Elliptic Sections
Journal of convex analysis, Tome 24 (2017) no. 2, pp. 685-693
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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.
Classification : 52A15, 53A04, 53A05
Mots-clés : Convex surface, quadric surface, quadric curve,planar section, characterization of ellipsoid 
@article{JCA_2017_24_2_JCA_2017_24_2_a19,
     author = {I. Arelio and L. Montejano},
     title = {Convex {Bodies} with {Many} {Elliptic} {Sections}},
     journal = {Journal of convex analysis},
     pages = {685--693},
     year = {2017},
     volume = {24},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_2_JCA_2017_24_2_a19/}
}
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I. Arelio; L. Montejano. Convex Bodies with Many Elliptic Sections. Journal of convex analysis, Tome 24 (2017) no. 2, pp. 685-693. http://geodesic.mathdoc.fr/item/JCA_2017_24_2_JCA_2017_24_2_a19/