Straffe Untermannigfaltigkeiten in konvexen Hyperflächen (Q1072123)

The author considers a tight substantial immersion \(f: M\to E^{n+m+2}\) of an \((n+m)\)-dimensional manifold with the same integral homology as \(S^ n\times S^ m\) such that the image of f lies in a strictly convex hypersurface. It is shown that f is projectively equivalent to the product of two convex hypersurfaces in \(E^{n+1}\) and \(E^{m+1}\). This extends and corrects an earlier statement by \textit{C.-S. Chen} [Am. J. Math. 101, 1083-1102 (1979; Zbl 0444.53039)]. For the case \(n=m\) and more generally for the case of tightly immersed and highly connected manifolds see the author's recent paper in Comment. Math. Helv. 61, 102-121 (1986).