{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,13]],"date-time":"2025-12-13T14:17:34Z","timestamp":1765635454778,"version":"3.48.0"},"reference-count":14,"publisher":"IOP Publishing","issue":"22","license":[{"start":{"date-parts":[[2020,10,27]],"date-time":"2020-10-27T00:00:00Z","timestamp":1603756800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2020,10,27]],"date-time":"2020-10-27T00:00:00Z","timestamp":1603756800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["UIDB\/MAT\/00212\/2020 UIDB\/MAT\/04561\/2020"],"award-info":[{"award-number":["UIDB\/MAT\/00212\/2020 UIDB\/MAT\/04561\/2020"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Class. Quantum Grav."],"published-print":{"date-parts":[[2020,11,19]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    In the cyclographic model of Laguerre geometry, the isotropy projection establishes a correspondence between submanifolds in the Lorentz (\n                    <jats:italic>n<\/jats:italic>\n                    + 1)-space and oriented hypersphere congruences in the Euclidean\n                    <jats:italic>n<\/jats:italic>\n                    -space. In this paper, we investigate the relation between the Lorentzian geometry of the sphere congruences and the Euclidean geometry of the corresponding oriented envelopes. We introduce the notion and discuss the existence of marginally outer trapped submanifolds associated to an (\n                    <jats:italic>n<\/jats:italic>\n                    \u2212 1)-dimensional Legendre submanifold of the unit tangent bundle over the Euclidean\n                    <jats:italic>n<\/jats:italic>\n                    -space. This extends the notion of Laguerre\u2013Gauss map of an oriented surface. Two special classes of marginally outer trapped surfaces are characterized in terms of their oriented envelopes. The Lorentzian geometry of several families of spheres whose envelopes are well-known surfaces in the Euclidean three-space is investigated.\n                  <\/jats:p>","DOI":"10.1088\/1361-6382\/abb957","type":"journal-article","created":{"date-parts":[[2020,9,17]],"date-time":"2020-09-17T18:15:28Z","timestamp":1600366528000},"page":"225016","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["On congruences of Laguerre cycles and their envelopes"],"prefix":"10.1088","volume":"37","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9578-2380","authenticated-orcid":false,"given":"R","family":"Pacheco","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7817-3989","authenticated-orcid":false,"given":"S D","family":"Santos","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2020,10,27]]},"reference":[{"volume":"vol 3","year":"1929","author":"Blaschke","key":"cqgabb957bib1","type":"book"},{"year":"1992","author":"Cecil","key":"cqgabb957bib2","type":"book"},{"year":"2011","author":"Chen","key":"cqgabb957bib3","type":"book"},{"key":"cqgabb957bib4","doi-asserted-by":"publisher","first-page":"551","DOI":"10.1088\/0264-9381\/24\/3\/003","type":"journal-article","article-title":"Marginally trapped surfaces in Lorentzian space forms with positive relative nullity","volume":"24","author":"Chen","year":"2007","journal-title":"Class. Quantum Grav."},{"key":"cqgabb957bib5","doi-asserted-by":"publisher","first-page":"1819","DOI":"10.1007\/s10714-008-0754-x","type":"journal-article","article-title":"Marginally trapped surfaces in Minkowski four-space invariant under a rotation subgroup of the Lorentz group","volume":"41","author":"Haesen","year":"2009","journal-title":"Gen. Relativ. Gravit."},{"key":"cqgabb957bib6","doi-asserted-by":"publisher","first-page":"5441","DOI":"10.1088\/0264-9381\/24\/22\/009","type":"journal-article","article-title":"Boost invariant marginally trapped surfaces in Minkowski four-space","volume":"24","author":"Haesen","year":"2007","journal-title":"Class. Quantum Grav."},{"key":"cqgabb957bib7","doi-asserted-by":"publisher","first-page":"1525","DOI":"10.1007\/s10114-005-0642-1","type":"journal-article","article-title":"Laguerre geometry of surfaces in R3","volume":"21","author":"Li","year":"2005","journal-title":"Acta Math. Sin."},{"key":"cqgabb957bib8","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1016\/j.geomphys.2015.06.009","type":"journal-article","article-title":"Marginally outer trapped surfaces in de Sitter space by low-dimensional geometries","volume":"96","author":"Musso","year":"2015","journal-title":"J. Geom. Phys."},{"year":"2019","author":"Musso","key":"cqgabb957bib9","type":"book"},{"key":"cqgabb957bib10","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/s00022-016-0334-2","type":"journal-article","article-title":"Evolutes of plane curves and null curves in Minkowski three-space","volume":"108","author":"Nolasco","year":"2017","journal-title":"J. Geom."},{"key":"cqgabb957bib11","doi-asserted-by":"publisher","first-page":"693","DOI":"10.1515\/forum-2019-0092","type":"journal-article","article-title":"Envelopes of circles and spacelike curves in the Lorentz-Minkowski three-space","volume":"32","author":"Pacheco","year":"2020","journal-title":"Forum Math."},{"key":"cqgabb957bib12","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1007\/s10711-019-00456-y","type":"journal-article","article-title":"Weierstrass-type representations","volume":"204","author":"Pember","year":"2020","journal-title":"Geometriae Dedicata"},{"key":"cqgabb957bib13","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1007\/bf01473438","type":"journal-article","article-title":"Dupin hypersurfaces","volume":"270","author":"Pinkall","year":"1985","journal-title":"Math. Ann."},{"key":"cqgabb957bib14","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/s0167-8396(97)00023-x","type":"journal-article","article-title":"Applications of Laguerre geometry in CAGD","volume":"15","author":"Pottmann","year":"1998","journal-title":"Comput. Aided Geomet. Des."}],"container-title":["Classical and Quantum Gravity"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/abb957","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/abb957\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/abb957","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/abb957\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/abb957\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/abb957","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/abb957\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/abb957\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/abb957\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/abb957\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/abb957\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/abb957","content-type":"text\/html","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,13]],"date-time":"2025-12-13T14:14:24Z","timestamp":1765635264000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/abb957"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,27]]},"references-count":14,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2020,10,27]]},"published-print":{"date-parts":[[2020,11,19]]}},"URL":"https:\/\/doi.org\/10.1088\/1361-6382\/abb957","relation":{},"ISSN":["0264-9381","1361-6382"],"issn-type":[{"type":"print","value":"0264-9381"},{"type":"electronic","value":"1361-6382"}],"subject":[],"published":{"date-parts":[[2020,10,27]]},"assertion":[{"value":"On congruences of Laguerre cycles and their envelopes","name":"article_title","label":"Article Title"},{"value":"Classical and Quantum Gravity","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2020 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2020-08-07","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2020-09-17","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2020-10-27","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}