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Generalisations of Robertson-Walker spaces. (English) Zbl 0998.53044
The paper enlarges the study of the 4-dimensional Robertson-Walker spacetimes from the point of view given by {\it R. Deszcz} and {\it W. Grycak} [Bull. Inst. Math. Acad. Sin. 15, 311-322 (1987; Zbl 0633.53031)], {\it F. Defever, R. Deszcz} and {\it M. Prvanovic} [Bull. Greek Math. Soc. 36, 43-62 (1994; Zbl 0923.53018)] and {\it R. Deszcz} and {\it M. Kucharski} [Tsukuba J. Math. 23, 113-130 (1999; Zbl 0965.53047)]. The main result of the paper provides that on a particular subclass of warped product manifolds, the same three curvature conditions of pseudosymmetry type are satisfied. Additionally an example of nontrivial such spaces is explicated.

53C50Lorentz manifolds, manifolds with indefinite metrics
53C80Applications of global differential geometry to physics