{"id":82,"date":"2018-11-09T11:50:17","date_gmt":"2018-11-09T13:50:17","guid":{"rendered":"http:\/\/www.professores.uff.br\/vitorbalestro\/?page_id=82"},"modified":"2018-11-09T11:50:17","modified_gmt":"2018-11-09T13:50:17","slug":"differential-geometry-of-immersed-surfaces-in-three-dimensional-normed-spaces","status":"publish","type":"page","link":"https:\/\/www.professores.uff.br\/vitorbalestro\/publications\/differential-geometry-of-immersed-surfaces-in-three-dimensional-normed-spaces\/","title":{"rendered":"Differential geometry of immersed surfaces in three-dimensional normed spaces"},"content":{"rendered":"<p id=\"h.p_OZGO5EFcBbOd\" class=\"zfr3Q\">V. Balestro, H. Martini and R. Teixeira,<strong> Differential geometry of immersed surfaces in three-dimensional normed spaces<\/strong>, preprint, 2018. (<a class=\"dhtgD\" href=\"https:\/\/www.google.com\/url?q=https%3A%2F%2Farxiv.org%2Fabs%2F1707.04226&amp;sa=D&amp;sntz=1&amp;usg=AFQjCNHi0c9R1j_qi8DOMAh0GIs4Leszkw\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv link<\/a>)<\/p>\n<p id=\"h.p_IffZGQHtBb4l\" class=\"zfr3Q\">Comments: The objective here is to develop an analogous theory to that of immersed surfaces in the Euclidean three-dimensional space for the case where the three-dimensional space is endowed with a general norm (sufficiently smooth and strictly convex, actually). There are two main concerns here: to define curvature and to understand how do the surface inherits the ambient metric. This paper is about the first question. The approach taken is inspired by affine differential geometry: the Birkhoff orthogonality relation given by the norm is used to define a transversal normal field on the immersed surface. This normal field &#8220;plays the role&#8221; of the Gauss map, and then analogous to principal curvatures are derived. Further on, using plane sections we define analogous to the normal curvature, and relate it to the principal curvatures.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>V. Balestro, H. Martini and R. Teixeira, Differential geometry of immersed surfaces in three-dimensional normed spaces, preprint, 2018. (arXiv link) Comments: The objective here is to develop an analogous theory to that of immersed surfaces in the Euclidean three-dimensional space for the case where the three-dimensional space is endowed with a general norm (sufficiently smooth [&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-82","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/82","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=82"}],"version-history":[{"count":1,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/82\/revisions"}],"predecessor-version":[{"id":83,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/82\/revisions\/83"}],"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=82"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/categories?post=82"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/tags?post=82"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}