Lorentzian para-Sasakian Manifolds with Generalized Symmetric Metric Connection

In this paper, we defined new metric connection for Lorentzian para-Sasakian manifolds which is called generalized symmetric metric connection of type $(\alpha,\beta)$. Quarter-symmetric and semi-symmetric connections are two samples of this connection such that $(\alpha,\beta)=(0,1)$ and $(\alpha,\beta)=(1,0)$, respectively. We get some basic concept with respect to generalized symmetric metric connection in a LP-Sasakian manifolds. Finally we consider CR-submanifolds with respect to generalized metric connection.