{"id":25279,"date":"2003-11-09T00:00:00","date_gmt":"2003-11-09T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/campos-de-vectores-harmonicos-killing\/"},"modified":"2003-11-09T00:00:00","modified_gmt":"2003-11-09T00:00:00","slug":"campos-de-vectores-harmonicos-killing","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/campos-de-vectores-harmonicos-killing\/","title":{"rendered":"Campos de vectores harm\u00f3nicos-killing"},"content":{"rendered":"<h2>Tesis doctoral de <strong>  P\u00e9rez L\u00f3pez M. Trinidad <\/strong><\/h2>\n<p>En este trabajo consideramos la harmonicidad del grupo 1-param\u00e9trico local de difeomorfismo asociado a un campo de vectores en una variedad (pseudo-)riemanniana lo que da lugar a las definiciones de campo de vectores harm\u00f3nico-killing y 1-harm\u00f3nico-killing. Para estos campos de vectores obtenemos resultados, cracterizaciones y ejemplos. Encontramos tambi\u00e9n la relaci\u00f3n existente entre estos nuevos campos de vectores y los ya cl\u00e1sicos campos de vectores killing, afines, conformes y proyectivos. Por otra parte damos respuesta a una conjectura formulada por k.Yano y t.Nagrano viendo que el flujo de los campos de jacobi a lo largo de la identidad no est\u00e1 formado por aplicaciones harm\u00f3nicas pero si por aplicaciones 1-harm\u00f3nicas (es decir, tan solo la parte lineal del campo de tensi\u00f3n se anula).  estudiamos los campos de vectores harm\u00f3nicos-killing en variedades kahler probando que en el caso compacto de vectores holomorfos.  en estas variedades estudiamos tambi\u00e9n los campos de vectores para los cuales el grupo 1-param\u00e9trico local de difeomorfismo est\u00e1 formado por aplicaciones pluriharm\u00f3nicas (1-pluriharm\u00f3nicas) a los que le llamamos campos de vectores pluriharm\u00f3nicos (resp. 1-pluriharm\u00f3nicos) y obtenemos para los mismos caracterizaciones, propiedades y ejemplos. Utilizando el formalismo clifford junto con la definici\u00f3n de aplicaci\u00f3n alpha-pluriharm\u00f3nica, siendo alpha una 2-forma harm\u00f3nica, extendemos la definici\u00f3n de campo de vectores pluriharm\u00f3nico a variedades (pseudo)-riemannianas no necesariamente kahler. En el caso kahler compacto probamos que todas las definiciones coinciden. Por \u00faltimo abrimos una nueva linea de investigaci\u00f3n en el caso (pseudo)-riemanniano pu\u00e9s son muchos los resultados de variedades riemannianas que no se pueden aplicar directamente al caso pseudo-riemaniano.  as\u00ed en una variedad riemanniana e imponiendo condiciones sobre la curvatura de ricci la f\u00f3rmula de bochner cl\u00e1sica proporciona res<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Campos de vectores harm\u00f3nicos-killing<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Campos de vectores harm\u00f3nicos-killing <\/li>\n<li><strong>Autor:<\/strong>\u00a0  P\u00e9rez L\u00f3pez M. Trinidad <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Santiago de compostela<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 11\/09\/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> V\u00e1zquez Abal M. Elena<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal:  Hervella torr\u00f3n Luis Mar\u00eda <\/li>\n<li> S\u00e1nchez valenzuela oscar adolfo (vocal)<\/li>\n<li> Dodson christopher terence john (vocal)<\/li>\n<li>Manuel De le\u00f3n rodr\u00edguez (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de P\u00e9rez L\u00f3pez M. Trinidad En este trabajo consideramos la harmonicidad del grupo 1-param\u00e9trico local de difeomorfismo asociado [&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":[583,127,126,977],"tags":[73789,27117,3233,73786,73788,73787],"class_list":["post-25279","post","type-post","status-publish","format-standard","hentry","category-geometria","category-geometria-de-riemann","category-matematicas","category-santiago-de-compostela","tag-dodson-christopher-terence-john","tag-hervella-torron-luis-maria","tag-manuel-de-leon-rodriguez","tag-perez-lopez-m-trinidad","tag-sanchez-valenzuela-oscar-adolfo","tag-vazquez-abal-m-elena"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/25279","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=25279"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/25279\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=25279"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=25279"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=25279"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}