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On Lorentzian \(\alpha\)-Sasakian manifolds. (English) Zbl 1085.53023
Let \(M^{2n+1}\) be a Lorentzian \(\alpha\)-Sasakian manifold. The authors prove that \(M\) is locally isometric to a sphere \(S^{2n+1}(\alpha^2)\) provided one of the following conditions holds: (1) \(M\) is conformally flat; (2) \(M\) is quasi-conformally flat; (3) \(R(X,Y)\cdot C = 0\), where \(R\) and \(C\) are the curvature tensor and conformal curvature tensor of \(M\), respectively.

MSC:
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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