Characterization of the Lorentzian para-Sasakian manifolds admitting a quarter-symmetric non-metric connection (original) (raw)

Some Classes of Lorentzian α-Sasakian Manifolds Admitting a Quarter-symmetric Metric Connection

2017

The object of the present paper is to study a quarter-symmetric metric connection in an Lorentzian α-Sasakian manifold. We study some curvature properties of an Lorentzian α-Sasakian manifold with respect to the quarter-symmetric metric connection. We study locally φ-symmetric, φsymmetric, locally projective φ-symmetric, ξ-projectively flat Lorentzian α-Sasakian manifold with respect to the quarter-symmetric metric connection.

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

Tbilisi Mathematical Journal, 2017

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 at, ϕ-symmetric, ϕ-projectively at Lorentzian α-Sasakian manifolds with respect to quartersymmetric metric connection. We also discuss Lorentzian α-Sasakian manifold admitting quarter-symmetric metric connection satisfying P̃.S̃ = 0, where P̃ denote the projective curvature tensor with respect to quarter-symmetric metric connection.

Some notes on LPLPLP-Sasakian Manifolds with Generalized Symmetric Metric Connection

Cornell University - arXiv, 2018

The present study initially identify the generalized symmetric connections of type (α, β), which can be regarded as more generalized forms of quarter and semi-symmetric connections. The quarter and semi-symmetric connections are obtained respectively when (α, β) = (1, 0) and (α, β) = (0, 1). Taking that into account, a new generalized symmetric metric connection is attained on Lorentzian para-Sasakian manifolds. In compliance with this connection, some results are obtained through calculation of tensors belonging to Lorentzian para-Sasakian manifold involving curvature tensor, Ricci tensor and Ricci semi-symmetric manifolds. Finally, we consider CR-submanifolds admitting a generalized symmetric metric connection and prove many interesting results.