Isometrische Immersionen der Kodimension 2 von Raumformen

Let M, resp. , denote Riemannian manifolds of dimensions m>4, resp. =m+2, and of constant sectional curvatures C, resp. , with denote an isometric immersion. Then the open subset of M consisting of all non-umbilic points of f is foliated by complete hypersurfaces of M, which are umbilical both in M and in . In this paper we study this foliation L in detail. In particular we prove: If in addition C>0 and is a standard space form, then the foliation L is a (globally) trivial fibre bundle with fibre S^m–1.