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We prove three facts about intrinsic geometry of surfaces in a normed Minkowski space. When put together, these facts demonstrate a rather intriguing picture. We show that 1 geodesics on saddle surfaces in a space of any dimension behave as they are expected to: they have no conjugate points and thus minimize length in their homotopy class; 2 in contrast, every two-dimensional Finsler manifold can be locally embedded as a saddle surface in a 4 —dimensional space; and 3 geodesics on convex surfaces in a 3 —dimensional space also behave as they are expected to: on a complete strictly convex surface, no complete geodesic minimizes the length globally.
Source Geom. Zentralblatt MATH identifier Keywords Finsler metric saddle surface convex surface geodesic. Burago, Dmitri; Ivanov, Sergei. On intrinsic geometry of surfaces in normed spaces.
Abstract Article info and citation First page References Abstract We prove three facts about intrinsic geometry of surfaces in a normed Minkowski space. Article information Source Geom. Export citation. Export Cancel. URL: Link to item. You have access to this content. You have partial access to this content. You do not have access to this content. More like this.
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We'd like to understand how you use our websites in order to improve them. Register your interest. The definition is based on averaging over small metric balls. This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Burago, Yu. Burago and S.