Abstract
The objective of the present paper is to study some newresults on para-Sasakian manifold with a quarter-symmetric metric connection. We classify the para-Sasakian manifold with respect to the quarter-symmetric metric connection satisfying the conditions (P) over bar.(N) over bar = 0, (R) over bar.(S) over bar = 0 and (S) over bar.(R) over bar = 0. Also, we obtain the conditions for the manifold with a quarter-symmetric metric connection to be xi-projectively flat and xi-conformally flat.