A generalization of Bonnet’s theorem on Darboux surfaces. (English. Russian original) Zbl 1315.53007

Math. Notes 95, No. 6, 760-767 (2014); translation from Mat. Zametki 95, No. 6, 812-820 (2014).
Summary: The well-known Bonnet theorem claims that, on a Darboux surface in three-dimensional Euclidean space, along each line of curvature, the corresponding principal curvature is proportional to the cube of another principal curvature. In the present paper, this theorem is generalized (with respect to dimension) to \(n\)-dimensional hypersurfaces of Euclidean spaces.


53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
53A05 Surfaces in Euclidean and related spaces
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