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 $(2n + 1)$-dimensional normal almost contact metric manifold, the Ricci operator $Q$ commutes with the structure tenso...
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| Date: | 2012 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2012
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2662 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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 $\phi$ 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. |
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