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On three-dimensional Lorentzian \(\alpha\)-Sasakian manifolds. (English) Zbl 1312.53071
Summary: The object of the present paper is to study three-dimensional Lorentzian \(\alpha\)-Sasakian manifolds which are Ricci-semisymmetry, locally \(\phi\)-symmetric and have \(\eta\)-parallel Ricci tensor. An example of a three-dimensional Lorentzian \(\alpha\)-Sasakian manifold is given which verifies all the theorems.

MSC:
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53D10 Contact manifolds (general theory)
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