## Some classes of Lorentzian $$\alpha$$-Sasakian manifolds admitting a quarter-symmetric metric connection.(English)Zbl 1365.53045

Summary: The object of the present paper is to study a quarter-symmetric metric connection in an Lorentzian $$\alpha$$-Sasakian manifold. We study some curvature properties of an Lorentzian $$\alpha$$-Sasakian manifold with respect to the quarter-symmetric metric connection. We study locally $$\phi$$-symmetric, $$\phi$$-symmetric, locally projective $$\phi$$-symmetric, $$\xi$$-projectively flat Lorentzian $$\alpha$$-Sasakian manifold with respect to the quarter-symmetric metric connection.

### MSC:

 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53B05 Linear and affine connections
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### References:

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