Characterization of the Lorentzian para-Sasakian manifolds admitting a quarter-symmetric non-metric connection

Abstract

We set the goal to study the properties of $LP$-Sasakian manifolds equipped with a quarter-symmetric non-metric connection. It is proved that the $LP$-Sasakian manifold endowed with a quarter-symmetric non-metric connection is partially Ricci semisymmetric with respect to the quarter-symmetric non-metric connection if and only if it is an $\eta$-Einstein manifold. We also study the properties of semisymmetric, Ricci recurrent $LP$-Sasakian manifolds and $\eta$-parallel Ricci tensor with respect to the quarter-symmetric non-metric connection. In the end, the non-trivial example of a $4$-dimensional $LP$-Sasakian manifold with a quarter-symmetric non-metric connection is given.