Some global aspects of compact space-times (Q796133)

Compact space-times M are considered for which the Ricci tensor satisfies \(Ric(X,X)>0\) for all nonspacelike \(X\neq 0\). It is shown that under this condition M does not admit any compact edgeless spacelike (or nontimelike) sections (in the sense of \textit{H.-J. Seifert} [Gen. Relativ. Gravitation 8, 815-831 (1977; Zbl 0425.53032)]). Furthermore through any two points of M there passes a closed timelike curve. The author indicates that the version of this last result under weaker conditions, given by \textit{F. J. Tipler} in his paper ''Singularities and causality violation'' [Ann. Phys. 108, 1-36 (1977; Zbl 0369.53057)], may contain an error in its proof.