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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Isometric homotopy in codimension two
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by John Douglas Moore PDF
Trans. Amer. Math. Soc. 292 (1985), 653-663 Request permission

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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Additional Information
  • © Copyright 1985 American Mathematical Society
  • 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