Geodesic
A Generalization of Bonnet's Theorem on Darboux Surfaces
Matematičeskie zametki, Tome 95 (2014) no. 6, pp. 812-820

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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.
Keywords: Bonnet theorem, Darboux surface, Euclidean space, line of curvature, principal curvature, Darboux tensor, Gaussian curvature.
Mots-clés : $n$-dimensional hypersurface 
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     author = {I. I. Bodrenko},
     title = {A {Generalization} of {Bonnet's} {Theorem} on {Darboux} {Surfaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {812--820},
     publisher = {mathdoc},
     volume = {95},
     number = {6},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_6_a1/}
}
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I. I. Bodrenko. A Generalization of Bonnet's Theorem on Darboux Surfaces. Matematičeskie zametki, Tome 95 (2014) no. 6, pp. 812-820. http://geodesic.mathdoc.fr/item/MZM_2014_95_6_a1/