Geodesic
Geometry of a~Doubly Canal Hypersurface in the~Euclidean Space~$\mathbb E^n$
Matematičeskie trudy, Tome 6 (2003) no. 1, pp. 169-181

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We consider a multidimensional analog in $\mathbb E^n$ to Dupin cyclides, that is, surfaces whose principal curvatures are constant along the corresponding principal directions. We study doubly canal hypersurfaces, i. e., hypersurfaces having two principal curvatures of multiplicities $p$ and $q$ with $p+q=n-1$. 
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     author = {M. A. Cheshkova},
     title = {Geometry of {a~Doubly} {Canal} {Hypersurface} in {the~Euclidean} {Space~}$\mathbb E^n$},
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M. A. Cheshkova. Geometry of a~Doubly Canal Hypersurface in the~Euclidean Space~$\mathbb E^n$. Matematičeskie trudy, Tome 6 (2003) no. 1, pp. 169-181. http://geodesic.mathdoc.fr/item/MT_2003_6_1_a6/