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Locally Convex Hypersurfaces

Published online by Cambridge University Press:  20 November 2018

L. B. Jonker  and
R. D. Norman
L. B. Jonker
Affiliation:
Queen's University, Kingston, Ontario
R. D. Norman
Affiliation:
Queen's University, Kingston, Ontario
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Let M be an n-dimensional connected topological manifold. Let ξ : M → Rn+1 be a continuous map with the following property: to each x ∈ M there is an open set x ∈ Ux ⊂ M, and a convex body Kx ⊂ Rn+1 such that ξ(UX) is an open subset of ∂Kx and such that is a homeomorphism onto its image. We shall call such a mapping ξ a locally convex immersion and, along with Van Heijenoort [8] we shall call ξ(M) a locally convex hypersurface of Rn+1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 3 , June 1973 , pp. 531 - 538
Copyright
Copyright © Canadian Mathematical Society 1973

References

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