{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/rigidity-results-on-gradient-schouten","title":"Rigidity results on gradient Schouten solitons","arxiv_id":"2010.06729","date":"2020-10-13","proceeding":null,"authors":["Romildo Pina","Ilton Menezes"],"abstract":"In this paper we consider $\\rho$-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.","url_abs":"http://arxiv.org/abs/2010.06729v1","url_pdf":"http://arxiv.org/pdf/2010.06729v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"rigidity-results-on-gradient-schouten","repo_url":"https://github.com/IltonMenezes/Ilton-Menezes-","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}