Codimension two submanifolds of positive curvature

Moore, John Douglas

doi:10.1090/S0002-9939-1978-0487560-8

Codimension two submanifolds of positive curvature
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Proc. Amer. Math. Soc. 70 (1978), 72-74 Request permission

Abstract:

In this note it is proven that a compact connected n-dimensional Riemannian manifold of positive curvature, isometrically immersed in $(n + 2)$ -dimensional Euclidean space, is a homotopy sphere if $n \geqslant 3$; hence it is homeomorphic to a sphere if $n \geqslant 5$.

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