A Classification of 3-dimensional Paracontact Metric Manifolds with $\varphi l=l\varphi$
Received:April 10, 2018  Revised:July 17, 2018
Key Word: paracontact metric manifold   para-Sasakian manifold   $\eta$-parallel Ricci tensor   cyclic $\eta$-parallel Ricci tensor
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11371076).
 Author Name Affiliation Quanxiang PAN School of Basical Science, Henan Institute of Techonology, Henan 453003, P. R. China Ximin LIU School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China
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Abstract:
Let $M^{3}$ be a 3-dimensional paracontact metric manifold. Firstly, a classification of $M^{3}$ satisfying $\varphi Q=Q\varphi$ is given. Secondly, manifold $M^{3}$ satisfying $\varphi l=l\varphi$ and having $\eta$-parallel Ricci tensor or cyclic $\eta$-parallel Ricci tensor is studied.
Citation:
DOI:10.3770/j.issn:2095-2651.2018.05.009