Geometry of a Doubly Canal Hypersurface in the Euclidean Space $\mathbb E^n$

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 $p+q=n-1$.