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Russian Mathematics

, Volume 63, Issue 1, pp 1–13 | Cite as

Normed Planes in Tangent Cone to Chord Space of Nonpositive Curvature

  • P. D. AndreevEmail author
  • V. V. StarostinaEmail author
Article
  • 7 Downloads

Abstract

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 words

chord space distinguished segments family basic chord non-positive curvature tangent cone normed plane weak convexity 

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Notes

Acknowledgments

Supported by Russian Foundation for Basic Research, grant No. 14-01-00219.

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Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Northern (Arctic) Federal University named after M. V. LomonosovArkhangelskRussia
  2. 2.Samara State University of Architecture and Civil EngineeringSamaraRussia

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