Abstract. The object of the present paper is to study certain curva-ture restriction on an LP-Sasakian manifold with a coefficient α . Amongothers it is shown that if an LP-Sasakian manifold with a coefficient α is a manifold of constant curvature, then the manifold is the productmanifold. Also it is proved that a 3-dimensional Ricci semisymmetricLP-Sasakian manifold with a constant coefficient α is a spaceform. 1. IntroductionIn 1989, Matsumoto [6] introduced the notion of LP-Sasakian manifolds.Then Mihai and Rosca [7] introduced the same notion independently and theyobtained several results in this manifold. In a recent paper, De, Shaikh, andSengupta [3] introduced the notion of LP-Sasakian manifolds with a coefficient α which generalizes the notion of LP-Sasakian manifolds. Recently, T. Ikawaand his coauthors [4], [5] studied Sasakian manifolds with Lorentzian metricand obtained several results in this manifold. The object of the present paperis to study certain curvature restriction on an LP-Sasakian manifold with acoefficient