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Let $M$ be a most singular orbit of the isotropy representation of a simplesymmetric space. Let $(\nu _i, \Phi _i)$ be an irreducible factor of the normalholonomy representation $(\nu _pM, \Phi (p))$. We prove that there exists abasis of a section $\Sigma _i\subset \nu _i$ of $\Phi _i$ such that thecorresponding shape operators have rational eigenvalues (this is not in generaltrue for other isotropy orbits). Conversely, this property, if referred to somenon-transitive irreducible normal holonomy factor, characterizes the isotropyorbits. We also prove that the definition of a submanifold with constantprincipal curvatures can be given by using only the traceless shape operator,instead of the shape operator, restricted to a non-transitive (non necessarilyirreducible) normal holonomy factor. This article generalizes previous resultsof the authors that characterized Veronese submanifolds in terms of normalholonomy.

Normal holonomy and rational properties of the shape operator