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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 R. Deszcz and W. Grycak [Bull. Inst. Math. Acad. Sin. 15, 311-322 (1987; Zbl 0633.53031)], F. Defever, R. Deszcz and M. Prvanovic [Bull. Greek Math. Soc. 36, 43-62 (1994; Zbl 0923.53018)] and R. Deszcz and 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.
MSC:
53C50Lorentz manifolds, manifolds with indefinite metrics
53C80Applications of global differential geometry to physics