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.References
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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