Convex solids whose point-source shadow-boundaries lie in hyperplanes
The light from any point source divides an ellipsoid into the bright and the dark halves, whose common boundary is contained in a hyperplane. This property characterizes ellipsoids among all convex bodies (i. e. bounded closed convex sets), see [\textit{T.~Kubota}, Lond. M. S. Proc. (2) 14, 230--239 (1915; JFM 45.1347.05)] for the 3-dimensional case and [\textit{G.~R.~Burton}, Isr. J. Math. 28, 339--349 (1977; Zbl 0368.52004)] for the general one. The author classifies unbounded closed convex sets, satisfying this property, and proves that such a set is either a convex component of a quadric, or the product of a 2-dimensional strictly convex set and an affine space, or the product of a 3-dimensional strictly convex cone and an affine space.
scientific article; zbMATH DE number 6121635