Normed Planes in Tangent Cone to Chord Space of Nonpositive Curvature
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We continue the cycle of papers devoted to study of the geometry of Busemann’s G-spaces with a distinguished family of segments (so-called chord spaces) which have non-positive curvature with respect to this family. We study the geometry of the tangent cone to chord space with non-positive curvature. It is shown that any two straight lines passing through the vertex of the cone span a weak normed plane, i.e., a weakly convex subset isometric to a plane with some norm.
Key wordschord space distinguished segments family basic chord non-positive curvature tangent cone normed plane weak convexity
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Supported by Russian Foundation for Basic Research, grant No. 14-01-00219.
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