{"id":117836,"date":"2015-10-07T00:00:00","date_gmt":"2015-10-07T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/closed-g2-forms-and-special-metrics\/"},"modified":"2015-10-07T00:00:00","modified_gmt":"2015-10-07T00:00:00","slug":"closed-g2-forms-and-special-metrics","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/geometria-de-riemann\/closed-g2-forms-and-special-metrics\/","title":{"rendered":"Closed g2 forms and special metrics"},"content":{"rendered":"

Tesis doctoral de Victor Manuel Manero Garcia <\/strong><\/h2>\n

En esta tesis se aborda el estudio y construcci\u00c2\u00bfn de variedades g2 calibradas. Una tal variedad es una variedad de riemann, de dimensi\u00c2\u00bfn 7, con una m\u00c2\u00bftrica de riemann definida por una cierta 3-forma diferencial, denominada g2 forma, la cual no s\u00c2\u00bflo es invariante por la acci\u00c2\u00bfn del grupo excepcional g2 sino que tambi\u00c2\u00bfn es cerrada y, por lo tanto, define una calibraci\u00c2\u00bfn en el sentido de harvey y lawson. Los dos primeros cap\u00c2\u00bftulos de esta memoria se dedican a la construcci\u00c2\u00bfn de nuevos ejemplos de esas variedades, tanto en el caso compacto como no-compacto. En particular, mostramos que el mapping torus de un difeomorfismo de una variedad half-flat simpl\u00c2\u00bfctica, tal que la estructura half-flat es preservada por el difeomorfismo, es una variedad g2 calibrada. En los cap\u00c2\u00bftulos 3 y 4 estudiamos la existencia de m\u00c2\u00bftricas especiales (einstein y ricci solitones) determinadas por g2 formas cerradas. Por una parte, sabemos que el comportamiento del tensor de ricci de la m\u00c2\u00bftrica inducida por una g2 forma est\u00c2\u00bf estrechamente relacionado con el comportamiento de la propia g2 forma. En particular, cleyton e ivanov probaron que ninguna variedad compacta, de dimensi\u00c2\u00bfn 7, admite una estructura g2 calibrada tal que la m\u00c2\u00bftrica inducida sea einstein, salvo que la g2 forma sea tambi\u00c2\u00bfn cocerrada y, por lo tanto, el grupo de holonom\u00c2\u00bfa de la m\u00c2\u00bftrica es un subgrupo de g2. En el cap\u00c2\u00bftulo 3 exploramos la versi\u00c2\u00bfn no compacta de este resultado, obteniendo un resultado equivalente para variedades (no compactas) resolubles.En el \u00c2\u00bfltimo cap\u00c2\u00bftulo, determinamos las nilvariedades compactas que poseen una g2 forma calibrada induciendo un nilsolit\u00c2\u00bfn. Para cada una de esas variedades, estudiamos el flujo laplaciano, y mostramos los primeros ejemplos compactos tales que la soluci\u00c2\u00bfn del flujo laplaciano est\u00c2\u00bf definida en un intervalo no acotado.<\/p>\n

 <\/p>\n

Datos acad\u00e9micos de la tesis doctoral \u00abClosed g2 forms and special metrics<\/strong>\u00ab<\/h3>\n
    \n
  • T\u00edtulo de la tesis:<\/strong>\u00a0 Closed g2 forms and special metrics <\/li>\n
  • Autor:<\/strong>\u00a0 Victor Manuel Manero Garcia <\/li>\n
  • Universidad:<\/strong>\u00a0 Pa\u00eds vasco\/euskal herriko unibertsitatea<\/li>\n
  • Fecha de lectura de la tesis:<\/strong>\u00a0 10\/07\/2015<\/li>\n<\/ul>\n

     <\/p>\n

    Direcci\u00f3n y tribunal<\/h3>\n
      \n
    • Director de la tesis<\/strong>\n
        \n
      • Mar\u00eda Luisa Fernandez Rodriguez<\/li>\n<\/ul>\n<\/li>\n
      • Tribunal<\/strong>\n
          \n
        • Presidente del tribunal: oscar Jes\u00fas Garay bengoechea <\/li>\n
        • vicente Cort\u00e9s (vocal)<\/li>\n
        • vicente Mu\u00f1oz velazquez (vocal)<\/li>\n
        • uwe Semmelmann — (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

           <\/p>\n","protected":false},"excerpt":{"rendered":"

          Tesis doctoral de Victor Manuel Manero Garcia En esta tesis se aborda el estudio y construcci\u00c2\u00bfn de variedades g2 calibradas. […]<\/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":[127,128,12909],"tags":[228030,228031,231983,231982,40331,231981],"class_list":["post-117836","post","type-post","status-publish","format-standard","hentry","category-geometria-de-riemann","category-geometria-diferencial","category-pais-vasco-euskal-herriko-unibertsitatea","tag-maria-luisa-fernandez-rodriguez","tag-oscar-jesus-garay-bengoechea","tag-uwe-semmelmann","tag-vicente-cortes","tag-vicente-munoz-velazquez","tag-victor-manuel-manero-garcia"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/117836","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=117836"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/117836\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=117836"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=117836"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=117836"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}