Isometric immersions in codimension two of warped products into space forms

Abstract

We provide a local classification of isometric immersions $f\colon L^p\times_ρM^n\to\Q_c^{p+n+k}$ in codimensions $k=1,2$ of warped products of Riemannian manifolds into space forms, under the assumptions that $n\ge k+1$ and that $N^{p+n}=L^p{\times }_{\rho }{M}^n$ has no points with the same constant sectional curvature $c$ as the ambient space form.

35 pages