Two special simply connected spaces of nonpositive curvature

V. K. Ionin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

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.

UDC: 514.17

Received: 30.01.2003

 English version: Siberian Mathematical Journal, 2003, 44:5, 807–812

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