  The present study initially identify the generalized symmetric connections of
type $(\alpha,\beta)$, which can be regarded as more generalized forms of
quarter and semi-symmetric connections. The quarter and semi-symmetric
connections are obtained respectively when $(\alpha,\beta)=(1,0)$ and
$(\alpha,\beta)=(0,1)$. 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.
