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Sibirskii Matematicheskii Zhurnal, 2003, Volume 44, Number 5, Pages 1033–1040 (Mi smj1227)  
Two special simply connected spaces of nonpositive curvature

V. K. Ionin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
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Abstract: We construct two examples of spaces homeomorphic to $\mathbb{R}^n(n\geqslant3)$ 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.
Keywords: metric, simplex, face, curvature, manifold, geodesic, space.
Received: 30.01.2003
English version:
Siberian Mathematical Journal, 2003, Volume 44, Issue 5, Pages 807–812
DOI: https://doi.org/10.1023/A:1025928502114
Bibliographic databases:
UDC: 514.17
Language: Russian
Citation: V. K. Ionin, “Two special simply connected spaces of nonpositive curvature”, Sibirsk. Mat. Zh., 44:5 (2003), 1033–1040; Siberian Math. J., 44:5 (2003), 807–812
Citation in format AMSBIB
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\jour Siberian Math. J.
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\pages 807--812
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