Reconstructing Isometry Groups From Killing Vector Fields

Reconstructing Isometry Groups From Killing Vector Fields | 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 Reconstructing Isometry Groups From Killing Vector Fields Thales B. S. F. Rodrigues, B. F. Rizzuti This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4319799/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 This work aims to explore a novel relation between Killing vector fields and Lie algebras using induced vector fields. On one hand, Killing vector fields on a (pseudo) Riemannian manifold are related to directions of local isometries along it. On the other hand, group elements are responsible for global isometries in physical systems, such as the elements of the groups \(SO(3)\) and \(SO(1,3)\) acting in space and space-time. In this sense, the main objective of this manuscript is to reconstruct such groups (together with translations), after establishing the connection between Killing vector fields and elements of the Lie algebra corresponding to such Lie groups, using mainly the definition of induced vector fields. Isometries Killing vector fields Lie algebras 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-4319799","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":295454812,"identity":"4457a23a-24aa-4b88-a1ab-e5acb3c02e28","order_by":0,"name":"Thales B. S. F. 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On one hand, Killing vector fields on a (pseudo) Riemannian manifold are related to directions of local isometries along it. On the other hand, group elements are responsible for global isometries in physical systems, such as the elements of the groups \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(SO(3)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(SO(1,3)\\)\u003c/span\u003e\u003c/span\u003e acting in space and space-time. 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