Geodesic
Normed planes in tangent cone to chord space of nonpositive curvature
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2019), pp. 3-17

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We continue the cycle of papers devoted to study of the geometry of Busemann's $G$-spaces with 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.
Keywords: chord space, distinguished segments family, basic chord, non-positive curvature, normed plane, weak convexity.
Mots-clés : tangent cone 
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     author = {P. D. Andreev and V. V. Starostina},
     title = {Normed planes in tangent cone to chord space of nonpositive curvature},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--17},
     publisher = {mathdoc},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_1_a0/}
}
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P. D. Andreev; V. V. Starostina. Normed planes in tangent cone to chord space of nonpositive curvature. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2019), pp. 3-17. http://geodesic.mathdoc.fr/item/IVM_2019_1_a0/