On gradient $ρ$-Einstein solitons with Bach tensor radially nonnegative
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913768675475456 |
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| author | Andrade, Maria Borges, Valter Reis, Hiuri |
| author_facet | Andrade, Maria Borges, Valter Reis, Hiuri |
| contents | In this paper, we study $n$-dimensional gradient $ρ$-Einstein solitons whose Bach tensor is radially nonnegative. Under this assumption, we show that such $ρ$-Einstein solitons are locally warped products of an interval and an Einstein manifold, provided either $ρ\neq0$ or $ρ=0$ and the soliton is rectifiable. We obtain as a consequence that these solitons must have harmonic Weyl tensor and vanishing Bach tensor. We also finish the classification of complete locally conformally flat steady $ρ$-Einstein solitons and classify these manifolds when their Bach tensor is radially nonnegative and $n\in\{3,4\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_24337 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On gradient $ρ$-Einstein solitons with Bach tensor radially nonnegative Andrade, Maria Borges, Valter Reis, Hiuri Differential Geometry Primary 35Q51, 53B20, 53C20, 53C25, Secondary 34A40 In this paper, we study $n$-dimensional gradient $ρ$-Einstein solitons whose Bach tensor is radially nonnegative. Under this assumption, we show that such $ρ$-Einstein solitons are locally warped products of an interval and an Einstein manifold, provided either $ρ\neq0$ or $ρ=0$ and the soliton is rectifiable. We obtain as a consequence that these solitons must have harmonic Weyl tensor and vanishing Bach tensor. We also finish the classification of complete locally conformally flat steady $ρ$-Einstein solitons and classify these manifolds when their Bach tensor is radially nonnegative and $n\in\{3,4\}$. |
| title | On gradient $ρ$-Einstein solitons with Bach tensor radially nonnegative |
| topic | Differential Geometry Primary 35Q51, 53B20, 53C20, 53C25, Secondary 34A40 |
| url | https://arxiv.org/abs/2503.24337 |