Abstract
We define the concept of a curvature netted hypersurface and investigate in what case the hypersurface is covered by a twisted product of spheres (or topological product of spheres). All hypersurfaces in a space form such that the number of mutually distinct principal curvatures is constant (i.e. each principal curvature has constant multiplicity) are curvature netted hypersurfaces. Also, we state some inductive constructions of the hypersurfaces, where we use the discussion related to the tube.
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Koike, N. The decomposition of curvature netted hypersurfaces. Geom Dedicata 54, 1–11 (1995). https://doi.org/10.1007/BF01265295
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DOI: https://doi.org/10.1007/BF01265295