Harmonic aspects in an $η$-Ricci soliton
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866916873837215744 |
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| author | Blaga, Adara M. |
| author_facet | Blaga, Adara M. |
| contents | We characterize $η$-Ricci solitons $(g,ξ,λ,μ)$ in some special cases when the $1$-form $η$, which is the $g$-dual of $ξ$, is a harmonic or a Schrödinger-Ricci harmonic form. We also provide necessary and sufficient conditions for $η$ to be a solution of the Schrödinger-Ricci equation and point out the relation between the three notions in our context. In particular, we apply these results to a perfect fluid spacetime and using Bochner- Weitzenböck techniques, we formulate some more conclusions for gradient solitons and deduce topological properties of the manifold and its universal covering. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_04679 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Harmonic aspects in an $η$-Ricci soliton Blaga, Adara M. Differential Geometry 35C08, 53C25 We characterize $η$-Ricci solitons $(g,ξ,λ,μ)$ in some special cases when the $1$-form $η$, which is the $g$-dual of $ξ$, is a harmonic or a Schrödinger-Ricci harmonic form. We also provide necessary and sufficient conditions for $η$ to be a solution of the Schrödinger-Ricci equation and point out the relation between the three notions in our context. In particular, we apply these results to a perfect fluid spacetime and using Bochner- Weitzenböck techniques, we formulate some more conclusions for gradient solitons and deduce topological properties of the manifold and its universal covering. |
| title | Harmonic aspects in an $η$-Ricci soliton |
| topic | Differential Geometry 35C08, 53C25 |
| url | https://arxiv.org/abs/1803.04679 |