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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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