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Proceedings of the American Mathematical Society

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Codimension two submanifolds of positive curvature

Author: John Douglas Moore
Journal: Proc. Amer. Math. Soc. 70 (1978), 72-74
MSC: Primary 53C40; Secondary 58E99
MathSciNet review: 487560
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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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Keywords: Submanifolds of positive curvature, Morse theory, isometric immersions
Article copyright: © Copyright 1978 American Mathematical Society