A non-immersion theorem for spaceforms
Let \(M(c)\) and \(\tilde M(\tilde c)\) be space forms of dimension m and \(2m-1\) respectively. Then the author proves that there exists no isometric immersion \(f: M\to \tilde M\) if (1) \(c<\tilde c\), \(c<0\) and M is fuchsian, or (2) \(0<c<\tilde c\). The proof is based on the observation that the space form M would admit a complete flat metric. Case (1) for \(\tilde c=0\) is due to \textit{F. Xavier} [Comment. Math. Helv. 60, 280-283 (1985; Zbl 0566.53045)] and case (2) is a result of \textit{J. D. Moore} [Pac. J. Math. 40, 157-166 (1972; Zbl 0238.53033)].
scientific article; zbMATH DE number 4069760