A Note on Lorenzian Para Sasakian Manifolds With an LP Contact Non-Metric Quarter Symmetric φ-Connection

In this paper, in a LP-Sasakian manifold M of dimension n(n=2m+1, m≥1), an affine connection, called an LP-contact non-metric quarter symmetric φ-connection has been introduced. It is shown that if the LP-Sasakian manifold of dimension n≥3 is Einstein and the curvature tensor of this new affine connection vanishes, then M is conformally flat if and only if it is flat, further some conditions are also obtained for M to be conformally flat. Finally a necessary condition is obtained for LP-contact manfold which admits LP-contact non-metric quarter symmetric φ-connection to be Sasakian.