<i>D</i>-homothetic deformation of normal almost contact metric manifolds
AbstractThe 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.
How to Cite
DeU. C., and GhoshS. “<i>D</I>-Homothetic Deformation of Normal Almost Contact Metric Manifolds”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 10, Oct. 2012, pp. 1330-29, http://umj.imath.kiev.ua/index.php/umj/article/view/2662.