Abstract
Let M be a closed manifold and let \(f:M \to \mathbb{R}^N\) be an immersion inducing a C2-smooth (respectively, polyhedral) metric of nonnegative curvature on M. If this nonnegativity property is preserved under all affine transformations of \(\mathbb{R}^N\), then f is an embedding into the boundary of a C2-smooth convex body (respectively, a convex polyhedron) in a certain \(\mathbb{R}^{n+1} \subset \mathbb{R}^N\). Bibliography: 6 titles.
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REFERENCES
A. D. Aleksandrov, “Ñber eine Verallgemeinerung der Riemannschen Geometrie” Schriftenreihe Inst. Math., No. 1, 38-84 (1957).
Yu. D. Burago and V. A. Zalgaller, “Suficient conditions of convexity” Zap. Nauchn. Semin. LOMI, 45, 3-52 (1974).
J. Milnor, Morse Theory (Ann. Math. Stud. 51), Princeton Univ. Press, Princeton, New Jersey (1963).
S. Sternberg, Lectures on Differential Geometry, Prentice Hall, Englewood Cliffs, New Jersey (1964).
S. Z. Shefel', “On two classes of k-surfaces in Euclidean n-space” Sib. Mat. Zh., 10, 459-466 (1969).
T. J. Willmore, Total Curvature in Riemannian Geometry, Ellis Horwood Limited (1982). 2864
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Lebedeva, N.D. Isometric Immersions of Closed Manifolds of Nonnegative Curvature. Journal of Mathematical Sciences 110, 2861–2864 (2002). https://doi.org/10.1023/A:1015362631423
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DOI: https://doi.org/10.1023/A:1015362631423