Some classes of Lorentzian α-Sasakian manifolds with respect to quarter-symmetric metric connection

Abstract

The object of the present paper is to study a quarter-symmetric metric connection in a Lorentzian α-Sasakian manifold. We study some curvature properties of Lorentzian α-Sasakian manifold with respect to quarter-symmetric metric connection. We investigate quasi-projectively flat, ϕ-symmetric, ϕ-projectively flat Lorentzian α-Sasakian manifolds with respect to quartersymmetric metric connection. We also discuss Lorentzian α-Sasakian manifold admitting quarter-symmetric metric connection satisfyingP .S = 0, whereP denote the projective curvature tensor with respect to quarter-symmetric metric connection.2010 Mathematics Subject Classification. 53C25. 53C15 Keywords. Quarter-symmetric metric connection, Lorentzian α-Sasakian manifold, quasi-projectively flat Lorentzian α-Sasakian manifold, ϕ-symmetric manifold, ϕ-projectively flat Lorentzian α-Sasakian manifold.

Some properties of trans Sasakian manifolds admitting a quarter-symmetric non-metric connection

“…A quarter-symmetric metric connection generalized a semi-symmetric connection which is introduced by Friedman and Schouten [11] in 1924. A quartersymmetric connection is further studied by many authors such as: Barman [2], Prakasha and Vikas [15], Singh [17,18,19], Prasad and Haseeb [16], Dey et al [8,9] etc.…”

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

“…Later, many geometers have studied Lorentzian α-Sasakian manifolds with different curvature restrictions in the papers [1,4,21,22] and others.…”