Codimension two product submanifolds with non-negative curvature

Abstract

We prove that if $f:M=M₁^n₁? M₂^n₂ → {R}ⁿ⁺²$ is an isometric immersion of a complete, non-compact Riemannian manifold M which is a product of non-negatively curved manifolds $M₁^n₁, n_i≥ 2$, $M₁$ non-flat and irreducible, then either f is $n₂$-cylindrical; or f is a product of hypersurface immersions with $M₁ \approx S^n₁$ or $R^n₁$; or f is $(n₂-1)$-cylindrical with $M₁\approx S^n₁$ or $RP²$ when $M₁$ is compact, and $M₁\approx R^n₁$ when $M₁$ is non-compact.