The index of the three orientable focal manifolds of isoparametric hypersurfaces in spheres with three principal curvatures equals the dimension of the ambient Euclidean space.
Mashimo,Spectra of the Laplacian on the Cayley projective plane, Tsukuba J
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The index of cubic focal manifolds
The index of the three orientable focal manifolds of isoparametric hypersurfaces in spheres with three principal curvatures equals the dimension of the ambient Euclidean space.