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Normed Planes in Tangent Cone to Chord Space of Nonpositive Curvature

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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.

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Acknowledgments

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

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Authors and Affiliations

  1. Northern (Arctic) Federal University named after M. V. Lomonosov, nab. Severnoi Dviny 17, Arkhangelsk, 163002, Russia

    P. D. Andreev

  2. Samara State University of Architecture and Civil Engineering, ul. Molodogvardeiskaya 194, Samara, 443001, Russia

    V. V. Starostina

Authors
  1. P. D. Andreev
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  2. V. V. Starostina
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Corresponding authors

Correspondence to P. D. Andreev or V. V. Starostina.

Additional information

Russian Text © P.D. Andreev, V.V. Starostina, 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 1, pp. 3–17.

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Andreev, P.D., Starostina, V.V. Normed Planes in Tangent Cone to Chord Space of Nonpositive Curvature. Russ Math. 63, 1–13 (2019). https://doi.org/10.3103/S1066369X19010018

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  • DOI: https://doi.org/10.3103/S1066369X19010018

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