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Transactions of the American Mathematical Society

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

 

 

Isometric homotopy in codimension two


Author: John Douglas Moore
Journal: Trans. Amer. Math. Soc. 292 (1985), 653-663
MSC: Primary 53C42
DOI: https://doi.org/10.1090/S0002-9947-1985-0808744-0
MathSciNet review: 808744
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Abstract: This article investigates the structure of the space of isometric immersions from a simply connected $ n$-dimensional Riemannian manifold with positive sectional curvatures into $ (n + 2)$-dimensional Euclidean space $ {E^{n + 2}}$. It is proven that if $ n \geqslant 4$ and $ {M^n}$ is such a manifold which admits a $ {C^\infty }$ isometric immersion as a hypersurface in $ {E^{n + 1}}$, then any $ {C^\infty }$ isometric immersion from $ {M^n}$ into $ {E^{n + 2}}$ is $ {C^{2n - 4}}$ homotopic through isometric immersions to an immersion whose image lies in some hyperplane.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0808744-0
Article copyright: © Copyright 1985 American Mathematical Society