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Some properties of Lorentzian \(\alpha \)-Sasakian manifolds with respect to quarter-symmetric metric connection. (English) Zbl 1346.53032
Summary: The aim of this paper is to study generalized recurrent, generalized Ricci-recurrent, weakly symmetric and weakly Ricci-symmetric, semi-generalized recurrent, semi-generalized Ricci-recurrent Lorentzian \(\alpha \)-Sasakian manifold with respect to quarter-symmetric metric connection. Finally, we give an example of 3-dimensional Lorentzian \(\alpha \)-Sasakian manifold with respect to quarter-symmetric metric connection.

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