Geodesic
On isometric immersion of closed manifolds of nonnegative curvature
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 4, Tome 261 (1999), pp. 187-193 
N. D. Lebedeva. On isometric immersion of closed manifolds of nonnegative curvature. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 4, Tome 261 (1999), pp. 187-193. http://geodesic.mathdoc.fr/item/ZNSL_1999_261_a12/
@article{ZNSL_1999_261_a12,
     author = {N. D. Lebedeva},
     title = {On isometric immersion of closed manifolds of nonnegative curvature},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {187--193},
     year = {1999},
     volume = {261},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_261_a12/}
}
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UR  - http://geodesic.mathdoc.fr/item/ZNSL_1999_261_a12/
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%V 261
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $M^n$ be a closed manifold. Assume that an immersion $f\colon M^n\to\mathbb R^N$ induces a $C^2$-smooth metric of nonnegative curvature or a polyhedral metric of nonnegative curvature on $M^n$. If this nonnegativness is left invariant under every affine transformation of $\mathbb R^N$, then $f$ is an embedding on the boundary of a $C^2$-smooth convex body (a convex polyhedron correspondingly) in some $\mathbb R^{n+1}\subset\mathbb R^N$.