Lorentzian para-Sasakian Manifolds Admitting a New Type of Quarter-symmetric Non-metric ξ-connection

Abstract

We define a new type of quarter-symmetric non-metric $\xi$-connection on an $LP$-Sasakian manifold and prove its existence. We provide its application in the general theory of relativity. To validate the existence of the quarter-symmetric non-metric $\xi$-connection on an $LP$-Sasakian manifold, we give a non-trivial example in dimension $4$ and verify our results.