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 – 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.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 10, pp. 1330–1345, October, 2012.
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De, U.C., Ghosh, S. D-Homothetic Deformation of Normal Almost Contact Metric Manifolds. Ukr Math J 64, 1514–1530 (2013). https://doi.org/10.1007/s11253-013-0732-7
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DOI: https://doi.org/10.1007/s11253-013-0732-7