Abstract
A closed convex surfaceS in\(\mathbb{E}^d \) is an ellipsoid if and only if for anyx, y εS there is an affinity mappingx ontoy and a neighborhood ofx inS onto a neighborhood ofy inS.
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Gruber, P.M., Ludwig, M. A Helmholtz-Lie type characterization of ellipsoids, II. Discrete Comput Geom 16, 55–67 (1996). https://doi.org/10.1007/BF02711133
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DOI: https://doi.org/10.1007/BF02711133