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Locally Convex Hypersurfaces

Canadian Journal of Mathematics, 1973
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.
Jonker, L. B., Norman, R. D.
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Hypersurface homogeneous and hypersurface self-similar models

Classical and Quantum Gravity, 1997
The field equation for hypersurface homogeneous models and hypersurface self-similar models in terms of variables associated with the symmetry surface are presented. In terms of these variables expressions are given for the kinematical quantities associated with the perfect fluid.
Nilsson, Ulf S., Uggla, Claes
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Hypersurfaces with Congruent Geodesics

Mathematische Nachrichten, 1992
It is the purpose of this paper to prove the following theorem: Let \(M\) be a compact hypersurface of a complete, simply connected space \(N\) of constant curvature, and suppose that all geodesics of \(M\) are congruent in \(N\). Then \(M\) is an extrinsic sphere of positive curvature. The article contains many nice geometric ideas.
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Dupin Hypersurfaces

Bulletin of the London Mathematical Society, 1983
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Hypersurfaces

1983
Kentaro Yano, Masahiro Kon
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