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Siberian Mathematical Journal

, Volume 44, Issue 5, pp 807–812 | Cite as

Two Special Simply Connected Spaces of Nonpositive Curvature

  • V. K. Ionin
Article
  • 16 Downloads

Abstract

We construct two examples of spaces homeomorphic to R n (n≥3) each of which has a closed geodesic and admits no isoperimetric inequality. The first is a complete polyhedral metric space of nonpositive curvature, and the second is an incomplete Riemannian space with nonpositive sectional curvatures.

metric simplex face curvature manifold geodesic space 

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References

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    Alexandrov A. D., Intrinsic Geometry of Convex Surfaces [in Russian], OGIZ, Moscow and Leningrad (1948).Google Scholar
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    Burago Yu. D. and Zalgaller V. A., Geometric Inequalities [in Russian], Nauka, Moscow (1980).Google Scholar
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    Ionin V. K., “Isoperimetric inequalities in simply connected Riemannian spaces of nonpositive curvature,” Dokl. Akad. Nauk SSSR, 203, No. 2, 282–284 (1972).Google Scholar
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    Einsenhart L. P., Riemannian Geometry [Russian translation], Izdat. Inostr. Lit., Moscow (1948).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • V. K. Ionin
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirsk

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