ABSTRACT
In the previous chapter we saw that orbits of s-representations agree, up to codimension two, with isoparametric submanifolds and their focal manifolds (or, equivalently, with submanifolds with constant principal curvatures). It is therefore natural to look for geometric invariants that distinguish orbits of s-representations from orbits of other representations (or submanifolds with constant principal curvatures from other submanifolds). In Chapters 3 and 4 we observed that the existence of a (nontrivial) parallel normal isoparametric section strongly influences the geometry of a submanifold.
