On gradient Riemann solitons invariant by rotation

On gradient Riemann solitons invariant by rotation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article On gradient Riemann solitons invariant by rotation Ilton Ferreira Menezes, Elismar Dias Batista, Willian Isao Tokura This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3848647/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this paper, we consider Riemann solitons that are conformal to an Euclidean space. Assuming that the solutions of the presented system of partial differential equations are invariant under the action of the orthogonal group, we provide all the solutions for the gradient Riemann solitons. We show that a gradient Riemann soliton (M, g) is both geodesically complete and rotationally symmetric if and only if g is the canonical product metric on R × S n−1 . Furthermore, this soliton is shrinking. Conformal metric scalar curvature Riemann solitons gradient Riemann solitons Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3848647","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":266207103,"identity":"0a654f51-7e14-4aa6-9e3f-7ba93605653c","order_by":0,"name":"Ilton Ferreira Menezes","email":"","orcid":"","institution":"Universidade Federal do Oeste da Bahia","correspondingAuthor":false,"prefix":"","firstName":"Ilton","middleName":"Ferreira","lastName":"Menezes","suffix":""},{"id":266207104,"identity":"a2b51f73-1442-4877-a181-d20999645d43","order_by":1,"name":"Elismar Dias Batista","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3UlEQVRIiWNgGAWjYDACdsYGEMW4gR1EG1gQoYUZpoXnAEiLBDFaIBTjBokEEE2EFn5m5uZPN2ruyW6XfH51w48CCQb+9u4EvFokmxnbpHOOFRvvnJ1TdrMH6DCJM2c34NVicJixjTmHLSFxw+2ctBs8QC0GErn4tdgfZmz+nPMPqOXmmbSbf4jRYgAMMencNqCWG+zHbhNliwTQYdK5fQnGO3ty2G7LGEjwEPQLf3v748853xJkt7Mff3bzzR8bOf72XvxakACPAZgkVjkIsD8gRfUoGAWjYBSMIAAAV4hI2eam5O4AAAAASUVORK5CYII=","orcid":"","institution":"Instituto Federal de Educação do Tocantins","correspondingAuthor":true,"prefix":"","firstName":"Elismar","middleName":"Dias","lastName":"Batista","suffix":""},{"id":266207105,"identity":"e1b5c630-8b48-407d-b84c-03161dc87388","order_by":2,"name":"Willian Isao Tokura","email":"","orcid":"","institution":"FACET, Universidade Federal da Grande Dourados","correspondingAuthor":false,"prefix":"","firstName":"Willian","middleName":"Isao","lastName":"Tokura","suffix":""}],"badges":[],"createdAt":"2024-01-09 15:29:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3848647/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3848647/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":50212386,"identity":"58cc9280-d612-413b-91bf-1d484df0adc8","added_by":"auto","created_at":"2024-01-26 12:07:28","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":251425,"visible":true,"origin":"","legend":"","description":"","filename":"ArticleTitle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3848647/v1_covered_33425bd2-b39c-4d76-9950-b69335ae0e41.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"On gradient Riemann solitons invariant by rotation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Conformal metric, scalar curvature, Riemann solitons, gradient Riemann solitons","lastPublishedDoi":"10.21203/rs.3.rs-3848647/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3848647/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we consider Riemann solitons that are conformal to an Euclidean space. 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