{"id":86,"date":"2018-11-09T11:54:20","date_gmt":"2018-11-09T13:54:20","guid":{"rendered":"http:\/\/www.professores.uff.br\/vitorbalestro\/?page_id=86"},"modified":"2018-11-09T11:56:56","modified_gmt":"2018-11-09T13:56:56","slug":"surface-immersions-in-normed-spaces-from-the-affine-point-of-view","status":"publish","type":"page","link":"https:\/\/www.professores.uff.br\/vitorbalestro\/publications\/surface-immersions-in-normed-spaces-from-the-affine-point-of-view\/","title":{"rendered":"Surface immersions in normed spaces from the affine point of view"},"content":{"rendered":"<p id=\"h.p_6ggx9diuDJrA\" class=\"zfr3Q\">V. Balestro, H. Martini and R. Teixeira, <strong>Surface immersions in normed spaces from the affine point of view<\/strong>, to appear in Geometriae Dedicata, 2018. (<a class=\"dhtgD\" href=\"https:\/\/www.google.com\/url?q=https%3A%2F%2Farxiv.org%2Fabs%2F1709.01397&amp;sa=D&amp;sntz=1&amp;usg=AFQjCNEecgLxnViLDIVGz3-YJ_GBKaE7eQ\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv link<\/a>) (<a class=\"dhtgD\" href=\"https:\/\/www.google.com\/url?q=https%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2Fs10711-018-0380-z&amp;sa=D&amp;sntz=1&amp;usg=AFQjCNF5FJJSHN2d93PajkXD5EfcFqx2ug\" target=\"_blank\" rel=\"noopener noreferrer\">journal link<\/a>)<\/p>\n<p id=\"h.p_Xi_zHFZfDLNt\" class=\"zfr3Q\">Comments: We&#8217;ve wrote a paper developing curvature concepts for surfaces immersed in three-dimensional spaces endowed with a norm (principal curvatures, Gaussian and mean curvatures, normal curvature). It turns out that the idea to do so came from affine differential geometry, and hence we naturally had a lot of questions related to this area within our context. We study affine distance functions, and from this we re-obtain some curvature concepts and also prove some rigidity theorems. We also introduce a Riemannian metric which is closely related to the induced geometry of the surface. Finally, we show in which cases the Birkhoff-Gauss map of a surface is the Blaschke vector field.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>V. Balestro, H. Martini and R. Teixeira, Surface immersions in normed spaces from the affine point of view, to appear in Geometriae Dedicata, 2018. (arXiv link) (journal link) Comments: We&#8217;ve wrote a paper developing curvature concepts for surfaces immersed in three-dimensional spaces endowed with a norm (principal curvatures, Gaussian and mean curvatures, normal curvature). It [&hellip;]<\/p>\n","protected":false},"author":205,"featured_media":0,"parent":12,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[],"tags":[],"class_list":["post-86","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/86","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/users\/205"}],"replies":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/comments?post=86"}],"version-history":[{"count":1,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/86\/revisions"}],"predecessor-version":[{"id":88,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/86\/revisions\/88"}],"up":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/12"}],"wp:attachment":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/media?parent=86"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/categories?post=86"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/tags?post=86"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}