{"id":112765,"date":"2012-04-06T00:00:00","date_gmt":"2012-04-06T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/clasificacion-de-toros-llanos-lorentzianos-en-espacios-tridimensionales\/"},"modified":"2012-04-06T00:00:00","modified_gmt":"2012-04-06T00:00:00","slug":"clasificacion-de-toros-llanos-lorentzianos-en-espacios-tridimensionales","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/geometria-diferencial\/clasificacion-de-toros-llanos-lorentzianos-en-espacios-tridimensionales\/","title":{"rendered":"Clasificaci\u00f3n de toros llanos lorentzianos en espacios tridimensionales."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Mar\u00eda  Amelia Leon Guzman <\/strong><\/h2>\n<p>Palabras clave:   superficies llanas lorentzianas, toros llanos lorentzianos, inmersiones isom\u00e9tricas, espacio anti-de sitter, toros de hopf, sumersiones de killing lorentzianas.  un problema cl\u00e1sico en geometr\u00eda lorentziana es la descripci\u00f3n de las inmersiones isom\u00e9tricas entre los espacios lorentzianos de curvatura constante. En este trabajo nos centramos en la clasificaci\u00f3n de las inmersiones isom\u00e9tricas del plano lorentziano en el espacio anti-de sitter tridimensional. Damos una f\u00f3rmula de representaci\u00f3n de estas inmersiones en t\u00e9rminos de pares de curvas (con posibles singularidades) en el plano hiperb\u00f3lico. Esto nos permite resolver los problemas propuestos por dajczer y nomizu en 1981.  de entre todas las inmersiones isom\u00e9tricas del plano lorentziano en el espacio anti-de sitter, algunas de ellas corresponden a toros lorentzianos (los ejemplos m\u00e1s sencillos son los toros de hopf). Como aplicaci\u00f3n de nuestra anterior descripci\u00f3n, probamos que todos estos toros pueden obtenerse a partir de dos curvas cerradas en el espacio hiperb\u00f3lico.  finalmente, demostramos que los toros de hopf son los \u00fanicos toros llanos lorentzianos inmersos en una amplia familia de sumersiones de killing lorentzianas tridimensionales.   keywords:  lorentzian flat surfaces, lorentzian flat tori, isometric immersions, anti de-sitter space, hopf tori, lorentzian killing submersions.  summary:  a classical problem in lorentzian geometry is the description of the isometric immersions between lorentzian spaces of constant curvature. We investigate the problem of classifying the isometric immersion from the lorentz plane into the three-dimensional anti-de sitter space, providing a representation formula of these isometric immersions in terms of pairs of curves (possibly with singularities) in the hyperbolic plane. We then give an answer to the open problems proposed by dajczer and nomizu in 1981.  among all isometric immersions of the lorentz plane into the anti-de sitter space, some of them are actually lorentzian tori (the basic examples are the hopf tori). As an application of our previous description, we prove that any such torus can be recovered from two closed curves in the hyperbolic plane.  finally, we prove that lorentzian hopf tori are the only immersed lorentzian flat tori in a wide family of lorentzian three-dimensional killing submersions.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Clasificaci\u00f3n de toros llanos lorentzianos en espacios tridimensionales.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Clasificaci\u00f3n de toros llanos lorentzianos en espacios tridimensionales. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Mar\u00eda  Amelia Leon Guzman <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Murcia<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 04\/06\/2012<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Pablo Mira Carrillo<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Luis jose Alias linares <\/li>\n<li>Juan  angel Aledo sanchez (vocal)<\/li>\n<li>ildefonso Castro l\u00f3pez (vocal)<\/li>\n<li>Jos\u00e9 Antonio Galvez lopez (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Mar\u00eda Amelia Leon Guzman Palabras clave: superficies llanas lorentzianas, toros llanos lorentzianos, inmersiones isom\u00e9tricas, espacio anti-de sitter, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[128,8235],"tags":[21824,181694,139256,8248,224213,139258],"class_list":["post-112765","post","type-post","status-publish","format-standard","hentry","category-geometria-diferencial","category-murcia","tag-ildefonso-castro-lopez","tag-jose-antonio-galvez-lopez","tag-juan-angel-aledo-sanchez","tag-luis-jose-alias-linares","tag-maria-amelia-leon-guzman","tag-pablo-mira-carrillo"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/112765","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=112765"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/112765\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=112765"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=112765"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=112765"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}