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\(\varphi\)-conformally flat Lorentzian para-Sasakian manifolds. (English) Zbl 1074.53057

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 \(\tau= n(n- 1)\).

MSC:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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