Codimension two product submanifolds with non-negative curvature
Abstract
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
,
non-flat and irreducible, then either f is
-cylindrical; or f is a product of hypersurface immersions with
or
; or f is
-cylindrical with
or
when
is compact, and
when
is non-compact.
![M<sub>1</sub><sup>n<sub>1</sub></sup>, n_i≥ 2](http://siba-ese.unile.it/plugins/generic/latexRender/cache/a8a87082a0f5c4a50100405fbce4541f.png)
![M<sub>1</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/cefe461b19878882eb4728e3a864a5da.png)
![n<sub>2</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/0258a41a55e6047808d2eee03142d24f.png)
![M<sub>1</sub> \approx S<sup>n<sub>1</sub></sup>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/4e59a16cd8903d46648e0dc6d82b67ba.png)
![R<sup>n<sub>1</sub></sup>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/4d81e7db043e65ebfa2bd2918c9dea06.png)
![(n<sub>2</sub>-1)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/5910d60c868e7966bda71f58885e4af0.png)
![M<sub>1</sub>\approx S<sup>n<sub>1</sub></sup>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/77ae01fad62b123d287aec0c6cca43be.png)
![RP<sup>2</sup>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/3c37a26eeb06c0681d2d1314d5c56c2d.png)
![M<sub>1</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/cefe461b19878882eb4728e3a864a5da.png)
![M<sub>1</sub>\approx R<sup>n<sub>1</sub></sup>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/65aa6c22c16af7ac9ebcdd7545a53599.png)
![M<sub>1</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/cefe461b19878882eb4728e3a864a5da.png)
DOI Code:
10.1285/i15900932v9n1p89
Full Text: PDF