D-homothetic deformation of normal almost contact metric manifolds

Abstract

The object of the present paper is to study a transformation called the $D$-homothetic deformation of normal almost contact metric manifolds. In particular, it is shown that, in a $(2n + 1)$-dimensional normal almost contact metric manifold, the Ricci operator $Q$ commutes with the structure tensor $\phi$ under certain conditions, and the operator $Q\phi - \phi Q$ is invariant under a $D$-homothetic deformation. We also discuss the invariance of $\eta$-Einstein manifolds, $\phi$-sectional curvature, and the local $\phi$-Ricci symmetry under a $D$-homothetic deformation. Finally, we prove the existence of such manifolds by a concrete example.