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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Nonnegatively curved submanifolds in codimension two


Author: Maria Helena Noronha
Journal: Trans. Amer. Math. Soc. 332 (1992), 351-364
MSC: Primary 53C40
DOI: https://doi.org/10.1090/S0002-9947-1992-1050086-9
MathSciNet review: 1050086
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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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DOI: https://doi.org/10.1090/S0002-9947-1992-1050086-9
Keywords: Curvature operator, soul, product of immersions, index of relativity nullity
Article copyright: © Copyright 1992 American Mathematical Society

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