{"id":433,"date":"2023-01-10T13:50:21","date_gmt":"2023-01-10T12:50:21","guid":{"rendered":"https:\/\/algant.apps.math.cnrs.fr\/\/?page_id=433"},"modified":"2024-06-23T14:37:03","modified_gmt":"2024-06-23T13:37:03","slug":"geometry","status":"publish","type":"page","link":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/cours\/geometry\/","title":{"rendered":"Geometry"},"content":{"rendered":"<p>Teachers: Laurent Bessi\u00e8res and Pierre Mounoud<\/p>\n<p><strong>Program:<\/strong><\/p>\n<ul>\n<li>Reminder of differential geometry: differential manifolds, tangent bundle, vector fields<\/li>\n<li>Riemannian metrics: connexions, parallel transport<\/li>\n<li>Geodesics: local existence and uniqueness, Gauss Lemma, completeness<\/li>\n<li>Curvatures: Riemann curvatures, Ricci curvature, scalar curvature<\/li>\n<li>Variational calculus and applications: variation formula for arclenght and energy, Jacobi fields<\/li>\n<li>Introduction to hyperbolic geometry<\/li>\n<\/ul>\n<p><strong>Prerequisites:<\/strong><\/p>\n<p>Differential Geometry.<\/p>\n<p><strong>References:<\/strong><\/p>\n<ul>\n<li>J. Cheeger, D. Ebin: Comparison theorems in Riemann Geometry (1975)<\/li>\n<li>M. Do Carmo: Riemannian Geometry (1992)<\/li>\n<li>S.Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry (1993)<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Teachers: Laurent Bessi\u00e8res and Pierre Mounoud Program: Reminder of differential geometry: differential manifolds, tangent bundle, vector fields Riemannian metrics: connexions, parallel transport Geodesics: local existence and uniqueness, Gauss Lemma, completeness Curvatures: Riemann curvatures, Ricci curvature, scalar curvature Variational calculus and applications: variation formula for arclenght and energy, Jacobi fields Introduction to hyperbolic geometry Prerequisites: Differential &hellip; <a href=\"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/cours\/geometry\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Geometry&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":4,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-433","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/433","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/comments?post=433"}],"version-history":[{"count":2,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/433\/revisions"}],"predecessor-version":[{"id":512,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/433\/revisions\/512"}],"up":[{"embeddable":true,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/4"}],"wp:attachment":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/media?parent=433"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}