On the immersion of an $n$-dimensional manifold in $n+1$-dimensional Euclidean space
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- by Benjamin Halpern PDF
- Proc. Amer. Math. Soc. 30 (1971), 181-184 Request permission
Abstract:
Consider the subset of $n + 1$-dimensional Euclidean space swept out by the tangent hyperplanes drawn through the points of an immersed compact closed connected n-dimensional smooth manifold. If this is not all of the Euclidean space, then the manifold is diffeomorphic to a sphere, the immersion is an embedding, the image of the immersion is the boundary of a unique open starshaped set, and the set of points not on any tangent hyperplane is the interior of the kernel of the open starshaped set. A converse statement also holds.References
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Benjamin Halpern, On the immersion of an n-dimensional manifold in $(n + 1)$ dimensional Euclidean space, Notices Amer. Math. Soc. 16 (1969), 774. Abstract #667-60.
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 181-184
- MSC: Primary 57.20
- DOI: https://doi.org/10.1090/S0002-9939-1971-0286116-3
- MathSciNet review: 0286116