Decomposable Elements In Eigenspaces Of The Curvature Operator Mariusz Frydrych Abstract. We find an algebraic obstruction preventing the flatness of the normal bundle of any isometric immersion of the Riemannian manifold $M$ into any space of constant sectional curvature $\kappa \in \Bbb R$ of an arbitrary dimension $N>\dim M$. The obstruction is expressed in terms of the curvature operator of the Riemannian manifold $M$. Keywords. Riemannian geometry, curvature operator. MS classification. 53C40, 58C25.