Conformally flat hypersurfaces in Euclidean 2-space. II (Q2574463)

In this paper the author studies generic conformally flat hypersurfaces in Euclidean space \(\mathbb R^4.\) The author defines a certain class \(\Theta\) of metrics for \(3\)-manifolds which includes all metrics for generic conformally flat hypersurfaces in \(\mathbb R^4.\) He obtains a kind of integrability condition on metrics of the class \(\Theta\) deriving a differential equation of order three and he proves some results for conformally flat hypersurfaces. He constructs new generic conformally flat hypersurfaces explicity giving some classification of all generic conformally flat hypersurfaces in \(\mathbb R^4.\) The new hypersurfaces are constructed from surfaces in \(\mathbb R^3 \) and \(S^3;\) some of them are of constant Gauss curvature. Part I, cf. [Nagoya Math. J. 158, 1--42 (2000; Zbl 1003.53043)]