D-Homothetic deformation of $LP$-Sasakian manifolds

Krishnendu De

The object of the present paper is to study a transformation called D-homothetic deformation of $LP$-Sasakian manifolds. Among others it is shown that in an $LP$-Sasakian manifold, the Ricci operator $Q$ commutes with the structure tensor $\phi $. We also discuss about the invariance of $\eta $-Einstein manifolds, $\phi $-sectional curvature, the locally $\phi $-Ricci symmetry and $\eta$-parallelity of the Ricci tensor under the D-homothetic deformation. Finally, we give an example of such a manifold.