{"id":4731,"date":"2024-12-19T04:39:45","date_gmt":"2024-12-19T04:39:45","guid":{"rendered":"https:\/\/science.sjp.ac.lk\/mat\/?page_id=4731"},"modified":"2024-12-19T04:40:22","modified_gmt":"2024-12-19T04:40:22","slug":"mat-484-2-0-differential-geometry-and-manifolds","status":"publish","type":"page","link":"https:\/\/science.sjp.ac.lk\/mat\/mat-484-2-0-differential-geometry-and-manifolds\/","title":{"rendered":"MAT 484 2.0 Differential Geometry and Manifolds"},"content":{"rendered":"<section class=\"wpb-content-wrapper\"><p>[vc_row][vc_column][vc_column_text]<\/p>\n<p><strong>Course:\u00a0\u00a0<\/strong>MAT 484 2.0 Differential Geometry and Manifolds (Optional)<\/p>\n\n<p><strong>Course Content<\/strong>:<\/p>\n\n<p style=\"text-align: justify;\">Regular curves; Local theory of curves parameterized by arc length; Global properties of plane curves; Isoperimetric inequality, four-vertex theorem; Regular surfaces; Tangent plane; Geometry of Gauss map; Ruled surfaces and minimal surfaces; The intrinsic geometry of surfaces; Gauss-Bonnet theorem and its applications; Introduction to manifolds; Riemannian manifolds, Tangent space, Riemannian metrics, Riemannian connection<\/p>\n\n<p><strong>Recommended Readings:<\/strong><\/p>\n\n\n<ol type=\"1\">\n<li style=\"list-style-type: none;\">\n<ol type=\"1\"><\/p>\n<li>Kuhnel W., Differential Geometry: Curves \u2013 Surfaces \u2013 Manifolds, third edition, American Mathematical Society, Vol. 77, 2015.<\/li>\n\n\n<li>Do Carmo M.P., Differential geometry of curves and surfaces, revised and updated second edition, Dover Publications, 2017.<\/li>\n\n\n<li>Shfrin T., DIFFERENTIAL GEOMETRY: A First Course in Curves and Surfaces Preliminary Version Summer, 2016<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n\n\n<p>&nbsp;<\/p>\n<p>[\/vc_column_text][\/vc_column][\/vc_row]<\/p>\n<\/section>","protected":false},"excerpt":{"rendered":"<p>[vc_row][vc_column][vc_column_text] Course:\u00a0\u00a0MAT 484 2.0 Differential Geometry and Manifolds (Optional) Course Content: Regular curves; Local theory of curves parameterized by arc length; Global properties of plane curves; Isoperimetric inequality, four-vertex theorem; Regular surfaces; Tangent plane; Geometry of Gauss map; Ruled surfaces and minimal surfaces; The intrinsic geometry of surfaces; Gauss-Bonnet theorem and its applications; Introduction to &hellip; <a href=\"https:\/\/science.sjp.ac.lk\/mat\/mat-484-2-0-differential-geometry-and-manifolds\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">MAT 484 2.0 Differential Geometry and Manifolds<\/span><\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_ti_tpc_template_sync":false,"_ti_tpc_template_id":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages\/4731"}],"collection":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/comments?post=4731"}],"version-history":[{"count":2,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages\/4731\/revisions"}],"predecessor-version":[{"id":4734,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages\/4731\/revisions\/4734"}],"wp:attachment":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/media?parent=4731"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}