On the metrics of the Riemannian manifolds which admit isometric imbedding into space of any constant curvature (Q1078817)

The author investigates analytic pseudo-Riemannian manifolds \(M^ n\) which can be immersed isometrically into spaces \(S^{n+1}(K)\) of every constant curvature K. He finds that \(M^ n\) has to be conformally flat, and he gives a local representation of the metric of \(M^ n\). The description of the result in the abstract of the paper, where \(S^{n+1}(K)\) is replaced by \(S^{n+p}(K)\), is obviously wrong as can easily be seen by the theorem of Nash.