Quarter-symmetric metric connection on a Lorentzian α-Sasakian manifold

Abstract

In the present paper we study locally ϕ-symmetric, locally projective ϕ-symmetric, ϕ-recurrent and ϕ-projectively flat Lorentzian α-Sasakian manifold with respect to quarter-symmetric metric connection. Further, the existence of a Lorentzian α-Sasakian manifold admitting quarter-symmetric metric connection is shown by constructing an example.