scholarly journals Locally convex hypersurfaces of negatively curved spaces

1977 ◽  
Vol 64 (2) ◽  
pp. 321-321 ◽  
Author(s):  
S. Alexander
Keyword(s):  
Curved Spaces ◽  
Negatively Curved ◽  
Locally Convex ◽  
Convex Hypersurfaces

scholarly journals Spheres and cells in negatively curved spaces

1967 ◽  
Vol 19 (4) ◽  
pp. 406-410 ◽  
Author(s):  
F. J. Flaherty
Keyword(s):  
Curved Spaces ◽  
Negatively Curved

Locally Convex Hypersurfaces

1973 ◽  
Vol 25 (3) ◽  
pp. 531-538 ◽  
Author(s):  
L. B. Jonker ◽  
R. D. Norman
Keyword(s):  
Convex Body ◽  
Open Subset ◽  
Convex Hypersurface ◽  
Topological Manifold ◽  
Continuous Map ◽  
Open Set ◽  
Locally Convex ◽  
Convex Hypersurfaces

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.

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