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Caustic of the three-dimensional ellipsoid. (Caustique de la surface ellipsoïdale à trois dimensions.) (French) Zbl 0951.53002

The authors study the normals of a 3-dimensional ellipsoid in 4-dimensional Euclidean space. The envelope of these normals is called caustic. The authors show, that this caustic is a hypersurface consisting of three parts, which intersect in four closed curves of hyperbolic umbilics. The considerations are based on the co-rank of a suitable mapping which is associated with the normals of the given ellipsoid.
Reviewer: O.Röschel (Graz)

MSC:

53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
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