$η$-Ricci solitons on para-Kenmotsu manifolds
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arXiv
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| Format: | Preprint |
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2014
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| _version_ | 1866909714261999616 |
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| author | Blaga, Adara M. |
| author_facet | Blaga, Adara M. |
| contents | In the context of paracontact geometry, $η$-Ricci solitons are considered on manifolds satisfying certain curvature conditions: $(ξ,\cdot)_{R}\cdot S=0$, $(ξ,\cdot)_{S}\cdot R=0$, $(ξ,\cdot)_{W_2}\cdot S=0$ and $(ξ,\cdot)_{S}\cdot W_2=0$. We prove that on a para-Kenmotsu manifold $(M,φ,ξ,η,g)$, the existence of an $η$-Ricci soliton implies that $(M,g)$ is quasi-Einstein and if the Ricci curvature satisfies $(ξ,\cdot)_{R}\cdot S=0$, then $(M,g)$ is Einstein. Conversely, we give a sufficient condition for the existence of an $η$-Ricci soliton on a para-Kenmotsu manifold. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1402_0223 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | $η$-Ricci solitons on para-Kenmotsu manifolds Blaga, Adara M. Differential Geometry In the context of paracontact geometry, $η$-Ricci solitons are considered on manifolds satisfying certain curvature conditions: $(ξ,\cdot)_{R}\cdot S=0$, $(ξ,\cdot)_{S}\cdot R=0$, $(ξ,\cdot)_{W_2}\cdot S=0$ and $(ξ,\cdot)_{S}\cdot W_2=0$. We prove that on a para-Kenmotsu manifold $(M,φ,ξ,η,g)$, the existence of an $η$-Ricci soliton implies that $(M,g)$ is quasi-Einstein and if the Ricci curvature satisfies $(ξ,\cdot)_{R}\cdot S=0$, then $(M,g)$ is Einstein. Conversely, we give a sufficient condition for the existence of an $η$-Ricci soliton on a para-Kenmotsu manifold. |
| title | $η$-Ricci solitons on para-Kenmotsu manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1402.0223 |