Generalized Robertson-Walker metrics and some of their properties. II (Q1074887)

[Part I, cf. Classical general relativity, Proc. Conf., London 1983, 63- 75 (1984; Zbl 0559.53012).] The paper generalizes previous results on Robertson-Walker (RW) space- times to arbitrary dimension and signature. A generalized RW manifold (GRW) is a manifold endowed with a metric g, which admits in local charts \((x^ 0,x^ i)_{1\leq i\leq n}\), the diagonal expression of the following type \[ g_{00}=e_ 0,\quad g_{ii}=e_ ie^{2T}(1+kr^ 2/4)^{-2}, \] with \[ e_ 0,e_ i=\pm 1,\quad \pm r^ 2\in \sum_{i}e_ i(X^ i)^ 2,\quad k=0,\pm 1, \] and where the function T depends only on \(x^ 0\). The paper shows that the three following conditions are equivalent: the GRW metrics are (a) expressible in \(x^ 0\)-independent form, (b) of constant curvature, (c) Einstein spaces. Moreover, the GRW metrics can be classified in six classes.