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.