Rigidity results on gradient Schouten solitons
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866913674257498112 |
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| author | Pina, Romildo Menezes, Ilton |
| author_facet | Pina, Romildo Menezes, Ilton |
| contents | In this paper we consider $ρ$-Einstein solitons of type $M= \left(B^n, g^{*}\right) \times (F^m,g_F)$, where $\left(B^n,g^{*}\right)$ is conformal to a pseudo-Euclidean space and invariant under the action of the pseudo-orthogonal group, and $\left(F^m,g_{F}\right)$ is an Einstein manifold. We provide all the solutions for the gradient Schouten soliton case. Moreover, in the Riemannian case, we prove that if
$M= \left(B^n, g^{*}\right) \times (F^m,g_F)$ is a complete gradient Schouten soliton then $\left(B^{n},g^{*}\right)$ is isometric to $\mathbb{S}^{n-1}\times \mathbb{R}$ and $F^m$ is a compact Einstein manifold. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2010_06729 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Rigidity results on gradient Schouten solitons Pina, Romildo Menezes, Ilton Differential Geometry Metric Geometry In this paper we consider $ρ$-Einstein solitons of type $M= \left(B^n, g^{*}\right) \times (F^m,g_F)$, where $\left(B^n,g^{*}\right)$ is conformal to a pseudo-Euclidean space and invariant under the action of the pseudo-orthogonal group, and $\left(F^m,g_{F}\right)$ is an Einstein manifold. We provide all the solutions for the gradient Schouten soliton case. Moreover, in the Riemannian case, we prove that if $M= \left(B^n, g^{*}\right) \times (F^m,g_F)$ is a complete gradient Schouten soliton then $\left(B^{n},g^{*}\right)$ is isometric to $\mathbb{S}^{n-1}\times \mathbb{R}$ and $F^m$ is a compact Einstein manifold. |
| title | Rigidity results on gradient Schouten solitons |
| topic | Differential Geometry Metric Geometry |
| url | https://arxiv.org/abs/2010.06729 |