Özgür, Cihan \(\varphi\)-conformally flat Lorentzian para-Sasakian manifolds. (English) Zbl 1074.53057 Rad. Mat. 12, No. 1, 99-106 (2003). The author proves the following results. Let \(M^n\) be an \(n\)-dimensional \((n> 3)\) Lorentzian para-Sasakian manifold. (1) If \(M^n\) is \(\varphi\)-conformally flat then \(M^n\) is an \(\eta\)-Einstein manifold. (2) If \(M^n\) is \(\varphi\)-conharmonically flat then \(M^n\) is an \(\eta\)-Einstein manifold with zero scalar curvature. (3) If \(M^n\) is \(\varphi\)-projectively flat then \(M^n\) is an Einstein manifold with scalar curvature \(\tau= n(n- 1)\). Reviewer: A. D. Osborne (Keele) Cited in 1 ReviewCited in 21 Documents MSC: 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) Keywords:\(\varphi\)-conformally flat; \(\varphi\)-conharmonically flat; \(\varphi\)-projectively flat; Lorentzian para-Sasakian manifold PDFBibTeX XMLCite \textit{C. Özgür}, Rad. Mat. 12, No. 1, 99--106 (2003; Zbl 1074.53057)