D-homothetic deformation of normal almost contact metric manifolds - De, U. C.; Ghosh, S. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
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 $φ$ under certain conditions, and the operator $Qφ - φ Q$ is invariant under a $D$-homothetic deformation. We also discuss the invariance of $η$-Einstein manifolds, $φ$-sectional curvature, and the local $φ$-Ricci symmetry under a $D$-homothetic deformation. Finally, we prove the existence of such manifolds by a concrete example.