On trivial gradient hyperbolic Ricci and gradient hyperbolic Yamabe solitons
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908474097532928 |
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| author | Blaga, Adara M. |
| author_facet | Blaga, Adara M. |
| contents | We provide conditions for a compact gradient hyperbolic Ricci and a compact gradient hyperbolic Yamabe soliton to be trivial, hence, the manifold to be an Einstein manifold in the first case, and a manifold of constant scalar curvature, in the second case. In particular, we prove that for a compact gradient hyperbolic Yamabe soliton of dimension $>2$, if the second Lie derivative of the metric in the direction of the potential vector field is trace-free and divergence-free, then the above conclusion is reached. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_09337 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On trivial gradient hyperbolic Ricci and gradient hyperbolic Yamabe solitons Blaga, Adara M. Differential Geometry We provide conditions for a compact gradient hyperbolic Ricci and a compact gradient hyperbolic Yamabe soliton to be trivial, hence, the manifold to be an Einstein manifold in the first case, and a manifold of constant scalar curvature, in the second case. In particular, we prove that for a compact gradient hyperbolic Yamabe soliton of dimension $>2$, if the second Lie derivative of the metric in the direction of the potential vector field is trace-free and divergence-free, then the above conclusion is reached. |
| title | On trivial gradient hyperbolic Ricci and gradient hyperbolic Yamabe solitons |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2311.09337 |