Bodrenko, I. I. 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. Cited in 1 Document MSC: 53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces 53A05 Surfaces in Euclidean and related spaces Keywords:Bonnet theorem; Darboux surface; Euclidean space; \(n\)-dimensional hypersurface; line of curvature; principal curvature; Darboux tensor; Gaussian curvature PDF BibTeX XML Cite \textit{I. I. Bodrenko}, Math. Notes 95, No. 6, 760--767 (2014; Zbl 1315.53007); translation from Mat. Zametki 95, No. 6, 812--820 (2014) Full Text: DOI References: [1] I. I. Bodrenko, Generalized Darboux Surfaces in the Spaces of Constant Curvature (LAP Lambert Acad. Publ., Saarbrücken, Germany, 2013). · Zbl 1366.53002 [2] V. F. Kagan, The Fundamentals of the Theory of Surfaces in Tensor Presentation, Part 2: Surfaces in Space. Transformations and Deformations of Surfaces. Special Questions (Gostekhizdat, Moscow-Leningrad, 1948) [in Russian]. [3] Yu. A. Aminov, “Condition of holonomicity of characteristic directions of a submanifold,” Mat. Zametki 41(4), 543-548 (1987) [Math. Notes 41 (4), 305-308 (1987)]. · Zbl 0625.53018 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.