Geodesic
Locally Convex Hypersurfaces
Canadian journal of mathematics, Tome 25 (1973) no. 3, pp. 531-538

Voir la notice de l'article provenant de la source Cambridge University Press

Let M be an n-dimensional connected topological manifold. Let ξ : M → R n+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 ⊂ R n+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 R n+1. 
Jonker, L. B.; Norman, R. D. Locally Convex Hypersurfaces. Canadian journal of mathematics, Tome 25 (1973) no. 3, pp. 531-538. doi: 10.4153/CJM-1973-054-7
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[1] 1. Busemann, H., Convex surfaces (Interscience Publishers, New York 1958). Google Scholar

[2] 2. Hartman, P. and Nirenberg, L., On spherical image maps whose Jacobians do not change sign, Amer. J. Math. 81 (1959), 901–920. Google Scholar

[3] 3. Hartman, P., On the isometric immersions in Euclidean space of manifolds with nonnegative sectional curvatures. II, Trans. Amer. Math. Soc. 11+7 (1970), 529-539. Google Scholar

[4] 4. Klee, V. L., jr., Convex sets in linear spaces, Duke Math. J. 18 (1951), 443–466. Google Scholar

[5] 5. Klee, V. L., jr., Extremal structure of convex sets. II, Math. Z. 69 (1958), 90–104. Google Scholar

[6] 6. Sacksteder, R., On hypersurfaces with no negative sectional curvatures, Amer. J. Math. 82 (1960), 609–630. Google Scholar

[7] 7. Valentine, F. A., Convex sets (McGraw-Hill, New York, 1964). Google Scholar

[8] 8. Van Heijenoort, J., On locally convex manifolds, Comm. Pure Appl. Math. 5 (1952), 223–242. Google Scholar

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