{"id":26751,"date":"2003-10-11T00:00:00","date_gmt":"2003-10-11T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/paralelismo-y-geodesicas-en-variedades-conformes\/"},"modified":"2003-10-11T00:00:00","modified_gmt":"2003-10-11T00:00:00","slug":"paralelismo-y-geodesicas-en-variedades-conformes","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/paralelismo-y-geodesicas-en-variedades-conformes\/","title":{"rendered":"Paralelismo y geod\u00e9sicas en variedades conformes"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Beatriz Salvador Allu\u00e9 <\/strong><\/h2>\n<p>Una variedad riemanniana tienen asociada una \u00fanica conexi\u00f3n lineal sim\u00e9trica-denominada de levi-civita- que respeta la estructura. Esta conexi\u00f3n es la herramienta fundamental para el estudio de esta geometr\u00eda, y permite en particular definir un paralelismo can\u00f3nico de vectores a lo largo de curvas.  la situaci\u00f3n no es la misma para el caso de una variedad conforme, pues de hecho existe toda una familia de conexiones sim\u00e9tricas compatibles con la estructura.  la aportaci\u00f3n original de esta tesis tiene su clave en el descubrimiento de un paralelismo can\u00f3nico definido sobre las curvas de una variedad conforme, construido mediante cierto criterio de adaptaci\u00f3n entre la curva y la familia completa de conexiones compatibles con la estructura conforme.  se ha denominado a este paralelismo \u00abde fermi-walker\u00bb, pues un paralelismo an\u00e1logo (con este nombre) ya fue utilizado como herramienta de estudio en relatividad general, en el contexto geom\u00e9trico de los espacios con estructura m\u00e9trica de lorentz.  la idea que subyace en este trabajo es la de mostrar c\u00f3mo el paralelismo fermi-walker puede desempe\u00f1ar para el estudio de la geometr\u00eda conforme un papel tan relevante como el que desempe\u00f1a la conexi\u00f3n de levi-civita para el estudio de la geometr\u00eda riemanniana.  en la tesis se describe c\u00f3mo el paralelismo fermi-walker produce una \u00abelevaci\u00f3n horizontal\u00bb sobre el fibrado de referencias lineales, de los vectores tangentes de segundo orden de la variedad conforme.  tambi\u00e9n se estudia en que forma esta \u00abconexi\u00f3n\u00bb ligada al segundo orden, permite reinterpretar los invariantes conformes cl\u00e1sicos de las curvas, con la ayuda de un nuevo invariante ligado al cl\u00e1sico tensor de schouten y a la propia conexi\u00f3n fermi-walker.  finalmente, se presenta una nueva noci\u00f3n de holonom\u00eda para variedades conformes, y se conjetura que est\u00e1 determinada por el tensor de curvatura de weyl. a modo de aproximaci\u00f3n se prueba que esta holonom\u00eda es<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Paralelismo y geod\u00e9sicas en variedades conformes<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Paralelismo y geod\u00e9sicas en variedades conformes <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Beatriz Salvador Allu\u00e9 <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Complutense de Madrid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 10\/11\/2003<\/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>Javier Lafuente L\u00f3pez<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal:  Amores l\u00e1zaro \u00e1ngel Miguel <\/li>\n<li>olga Gil medrano (vocal)<\/li>\n<li>Fernando Etayo gordejuela (vocal)<\/li>\n<li>ignacio S\u00e1nchez rodr\u00edguez (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Beatriz Salvador Allu\u00e9 Una variedad riemanniana tienen asociada una \u00fanica conexi\u00f3n lineal sim\u00e9trica-denominada de levi-civita- que respeta [&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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