D-Homothetic Deformation of Normal Almost Contact Metric Manifolds

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 (2 n +1)-dimensional normal almost contact metric manifold, the Ricci operator Q commutes with the structure tensor ϕ under certain conditions, and the operator Qϕ – ϕQ 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 the D -homothetic deformation. Finally, we prove the existence of these manifolds by a concrete example.