Nonnegatively curved submanifolds in codimension two

Noronha, Maria Helena

doi:10.1090/S0002-9947-1992-1050086-9

Nonnegatively curved submanifolds in codimension two
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Trans. Amer. Math. Soc. 332 (1992), 351-364 Request permission

Abstract:

Let $M$ be a complete noncompact manifold with nonnegative sectional curvatures isometrically immersed in Euclidean spaces with codimension two. We show that $M$ is a product over its soul, except when the soul is the circle ${S^1}$ or $M$ is $3$-dimensional and the soul is the Real Projective Plane. We also give a rather complete description of the immersion, including the exceptional cases.

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