{"id":33808,"date":"1998-01-01T00:00:00","date_gmt":"1998-01-01T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/estudio-del-operador-de-jacobi-en-geometria-semi-riemanniana\/"},"modified":"1998-01-01T00:00:00","modified_gmt":"1998-01-01T00:00:00","slug":"estudio-del-operador-de-jacobi-en-geometria-semi-riemanniana","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/estudio-del-operador-de-jacobi-en-geometria-semi-riemanniana\/","title":{"rendered":"Estudio del operador de jacobi en geometria semi-riemanniana."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Ram\u00f3n Lorenzo V\u00e1zquez <\/strong><\/h2>\n<p>En la memoria se estudian los operadores de jacobi en variedades semi-riemannianas desde dos puntos de vista.  por un lado se analiza la constancia de los autovalores de dichos operadores y, por otra parte, se estudian ciertos casos en los que los operadores de jacobi presentan un autoespacio distinguido. As\u00ed, en el cap\u00edtulo 1 se analiza la situaci\u00f3n de estos dos problemas en los marcos riemanniano y lorentziano, como paso previo al estudio del caso semi-riemanniano.  en cuanto al estudio de los autovalores, estrechamente relacionado con el problema de osserman, en el cap\u00edtulo 2 se construyen varias familias de nuevos ejemplos de espacios de osserman semi-riemannianos. En concreto, se muestra la mayor complejidad y la existencia de profundas diferencias en el estudio de la condici\u00f3n de osserman en geometr\u00eda semi-riemanniana, construyendo variedades de osserman con m\u00e9trica de cualquier signatura (p,q), p,q mayor o igual a 2, que no son localmente sim\u00e9tricas (en realidad, ni siquiera localmente homog\u00e9neas). Estos nuevos ejemplos motivan el estudio de una clase particular de espacios de osserman: las variedades de osserman especiales, mostr\u00e1ndose en el tercer cap\u00edtulo que son localmente sim\u00e9tricas y clasific\u00e1ndolas cuando la dimnesi\u00f3n es distinta de 16 y 32.  en esta clasificaci\u00f3n aparecen cuatro familias de variedades de osserman especiales. Para dos de ellas, las variedades kahler indefinidas de curvatura seccional holomorfa constante y las variedades cuaterni\u00f3nicas kahler indefinidas de curvatura seccional cuaterni\u00f3nica constante, diversos autores han analizado la constancia de la curvatura a partir de la existencia de autoespacios distinguidos de los operadores de jacobi. La no existencia de estudios similares para las otras dos familias, las variedades para-kahler de curvatura seccional paraholomorfa constante y las variedades paracuaterni\u00f3nicas kahler de curvatura seccional paracuaterni\u00f3nica constante, mot<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Estudio del operador de jacobi en geometria semi-riemanniana.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Estudio del operador de jacobi en geometria semi-riemanniana. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Ram\u00f3n Lorenzo V\u00e1zquez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Santiago de compostela<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/01\/1998<\/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>Regina Castro Bola\u00f1o<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal:  Cordero Rego Luis Angel <\/li>\n<li>Antonio Diaz Miranda (vocal)<\/li>\n<li>Lieven Vanhecke (vocal)<\/li>\n<li>Manuel Barros Diaz (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Ram\u00f3n Lorenzo V\u00e1zquez En la memoria se estudian los operadores de jacobi en variedades semi-riemannianas desde dos [&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 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