Codimension two submanifolds of positive curvature
Author:
John Douglas Moore
Journal:
Proc. Amer. Math. Soc. 70 (1978), 72-74
MSC:
Primary 53C40; Secondary 58E99
DOI:
https://doi.org/10.1090/S0002-9939-1978-0487560-8
MathSciNet review:
487560
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Abstract | References | Similar Articles | Additional Information
Abstract: In this note it is proven that a compact connected n-dimensional Riemannian manifold of positive curvature, isometrically immersed in -dimensional Euclidean space, is a homotopy sphere if
; hence it is homeomorphic to a sphere if
.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1978-0487560-8
Keywords:
Submanifolds of positive curvature,
Morse theory,
isometric immersions
Article copyright:
© Copyright 1978
American Mathematical Society