{"id":513,"date":"2025-03-29T21:09:36","date_gmt":"2025-03-29T19:09:36","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/gentle\/?p=513"},"modified":"2025-09-10T07:18:10","modified_gmt":"2025-09-10T05:18:10","slug":"flat-generalized-connections-on-courant-algebroids","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/gentle\/2025\/03\/29\/flat-generalized-connections-on-courant-algebroids\/","title":{"rendered":"Flat Generalized Connections on Courant Algebroids"},"content":{"rendered":"<p>Paper by G. Cavalcanti, J. Pedregal and R. Rubio.<\/p>\n<p><a href=\"_wp_link_placeholder\" data-wplink-edit=\"true\">Selecta Math. (N.S.)<span data-test=\"journal-volume\"> 31 (2025)<\/span>, no. 5, article number <span data-test=\"article-number\">84<\/span>, 34pp<\/a>.<\/p>\n<p>Abstract: We consider a family of metric generalized connections on transitive Courant algebroids, which includes the canonical Levi-Civita connection, and study the flatness condition. We find that the building blocks for such flat transitive Courant algebroids are compact simple Lie groups. Further, we give a description of left-invariant flat Levi-Civita generalized connections on such Lie groups, which, in particular, shows the existence of non-flat ones.<\/p>\n<p>Find it also on the <a href=\"https:\/\/arxiv.org\/abs\/2503.21881\">arxiv (2503.21881)<\/a><\/p>\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"561\" height=\"929\" src=\"https:\/\/mat.uab.cat\/web\/gentle\/wp-content\/uploads\/sites\/38\/2025\/03\/image-1.png\" alt=\"\" class=\"wp-image-618\" srcset=\"https:\/\/mat.uab.cat\/web\/gentle\/wp-content\/uploads\/sites\/38\/2025\/03\/image-1.png 561w, https:\/\/mat.uab.cat\/web\/gentle\/wp-content\/uploads\/sites\/38\/2025\/03\/image-1-181x300.png 181w\" sizes=\"auto, (max-width: 561px) 100vw, 561px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Paper by G. Cavalcanti, J. Pedregal and R. Rubio. Selecta Math. (N.S.) 31 (2025), no. 5, article number 84, 34pp. Abstract: We consider a family of metric generalized connections on transitive Courant algebroids, which includes the canonical Levi-Civita connection, and study the flatness condition. We find that the building blocks for such flat transitive Courant [&hellip;]<\/p>\n","protected":false},"author":54,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[51,32,34],"tags":[],"class_list":["post-513","post","type-post","status-publish","format-standard","hentry","category-papers","category-pedregal","category-rubio"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts\/513","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/users\/54"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/comments?post=513"}],"version-history":[{"count":7,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts\/513\/revisions"}],"predecessor-version":[{"id":621,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts\/513\/revisions\/621"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/media?parent=513"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/categories?post=513"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/tags?post=513"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}