Codimension two product submanifolds with non-negative curvature


We prove that if(Error rendering LaTeX formula) is an isometric immersion of a complete, non-compact Riemannian manifold M which is a product of non-negatively curved manifolds M<sub>1</sub><sup>n<sub>1</sub></sup>, n_i≥ 2, M<sub>1</sub> non-flat and irreducible, then either f is n<sub>2</sub>-cylindrical; or f is a product of hypersurface immersions with M<sub>1</sub> \approx S<sup>n<sub>1</sub></sup> or R<sup>n<sub>1</sub></sup>; or f is (n<sub>2</sub>-1)-cylindrical with M<sub>1</sub>\approx S<sup>n<sub>1</sub></sup> or RP<sup>2</sup> when M<sub>1</sub> is compact, and M<sub>1</sub>\approx R<sup>n<sub>1</sub></sup> when M<sub>1</sub> is non-compact.

DOI Code: 10.1285/i15900932v9n1p89

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