Isometric immersions of closed manifolds of nonnegative curvature
The author extends a result of \textit{S. Z. Shefel}' [Sib. Mat. Zh. 10, 459-466 (1969; Zbl 0174.53101)] by proving that if \(M\) is a closed \(n\)-manifold and \(f:M\to \mathbb{R}^N\) an immersion inducing a \(C^2\)-smooth (or polyhedral) metric of nonnegative curvature on \(M\), and such that this nonnegativity property is preserved under composition with all affine transformations of \(\mathbb{R}^N\), then \(f\) is an embedding and \(f(M)\) is a \(C^2\)-smooth convex body (or polyhedron) in \(\mathbb{R}^{n+1}\).
scientific article; zbMATH DE number 1777776