{"id":128481,"date":"1996-01-01T00:00:00","date_gmt":"1996-01-01T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/matrices-de-gram-y-espacios-de-angulos-diedricos-de-poliedros\/"},"modified":"1996-01-01T00:00:00","modified_gmt":"1996-01-01T00:00:00","slug":"matrices-de-gram-y-espacios-de-angulos-diedricos-de-poliedros","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/matrices-de-gram-y-espacios-de-angulos-diedricos-de-poliedros\/","title":{"rendered":"Matrices de gram y espacios de angulos diedricos de poliedros."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Raquel Diaz Sanchez <\/strong><\/h2>\n<p>La memoria esta motivada por el \u00abteorema de andreev generalizado\u00bb, es decir, la descripcion del espacio de angulos diedricos de poliedros compactos hiperbolicos de un tipo combinatorio determinado. El teorema de andreev describe este espacio cuando se impone la restriccion de que todos los angulos sean menores o iguales que  \/2. La forma de tratar el problema es utilizando la matriz de gram del poliedro.  se obtiene una caracterizacion de las matrices que son matrices de gram de d-politopos (los objetos analogos a los poliedros en dimension arbitraria) en un espacio geometrico que puede ser esferico o hiperbolico. En el caso hiperbolico se tiene tambien una caracterizacion para los politopos compactos.  utilizando esta caracterizacion de matrices de gram se obtiene el teorema de andreev generalizado para los descendientes de tetraedros, es decir, la familia de poliedros que se obtienen del tetraedro truncando vertices sucesivamente. En particular, para el primer poliedro de esta familia, el prisma triengular, se dan explicitamente las ecuaciones e inecuaciones que describen el espacio de angulos diedricos.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Matrices de gram y espacios de angulos diedricos de poliedros.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Matrices de gram y espacios de angulos diedricos de poliedros. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Raquel Diaz Sanchez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Complutense de Madrid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/01\/1996<\/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>Enrique Arrondo Esteban<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal:  Ruiz Sancho Jes\u00fas Mar\u00eda <\/li>\n<li>Igor Rivin (vocal)<\/li>\n<li>Antonio  F\u00e9lix Costa Gonz\u00e1lez (vocal)<\/li>\n<li> Lozano Imizcoz M. Teresa (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Raquel Diaz Sanchez La memoria esta motivada por el \u00abteorema de andreev generalizado\u00bb, es decir, la descripcion [&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":[986,583,46357,126],"tags":[23287,64393,241726,241727,241725,35551],"class_list":["post-128481","post","type-post","status-publish","format-standard","hentry","category-complutense-de-madrid","category-geometria","category-geometrias-no-euclideas","category-matematicas","tag-antonio-felix-costa-gonzalez","tag-enrique-arrondo-esteban","tag-igor-rivin","tag-lozano-imizcoz-m-teresa","tag-raquel-diaz-sanchez","tag-ruiz-sancho-jesus-maria"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/128481","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=128481"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/128481\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=128481"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=128481"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=128481"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}