The mobility of Riemannian spaces with respect to conformal mappings onto Einstein spaces (Q619468)

\textit{H. W. Brinkmann} [Math. Ann. 94, 117--145 (1925; JFM 51.0568.03)] reduced the question whether a Riemannian space admits a conformal mapping onto some Einstein space to the problem of existence of a solution for a Cauchy-type nonlinear system of differential equations. In this paper, the authors estimate the first lacuna in the distribution of mobility degrees \(r\) of \(n\)-dimensional (pseudo-)Riemannian spaces with respect to conformal mappings onto Einstein spaces. They obtain a tensor characteristic of spaces which are not conformally flat and have \(r = n - 1\), which is the maximum possible value. Thus, maximum mobile nonconformally flat spaces with \(r = n - 1\) are found.