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Two-dimensional finite non-positively curved polyhedra of rank two. (Polyèdres finis de dimension 2 à courbure \(\leq 0\) et de rang 2.) (French) Zbl 0831.53031
Summary: We locally define the notion of polyhedra of rank two for two-dimensional finite non-positively curved polyhedra. We prove that the universal covering of such a space is either the product of two trees or an Euclidean Tits building of rank two.

53C35 Differential geometry of symmetric spaces
51E24 Buildings and the geometry of diagrams
51M20 Polyhedra and polytopes; regular figures, division of spaces
20E42 Groups with a \(BN\)-pair; buildings
05C12 Distance in graphs
Full Text: DOI Numdam EuDML
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[2] K.S. BROWN, Buildings, Springer-Verlag, New York, 1989. · Zbl 0715.20017
[3] K.S. BROWN, Five lectures on buildings, Congrès de Trieste 1990. · Zbl 0846.20032
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[5] W. BALLMANN, M. BRIN, R. SPATZIER, Structure of manifolds of nonpositive curvature. II, Annals of Mathematics, 122 (1985), 205-235. · Zbl 0598.53046
[6] K. BURNS, R. SPATZIER, Manifolds of nonpositive curvature and their buildings, Publications Mathématiques de l’IHES, n° 65, 1987. · Zbl 0643.53037
[7] W. BALLMANN, S. BUYALO, Nonpositive curved metrics on 2-polyedra, Bonn, février 1994.
[8] M. BRIDSON, A. HAEFLIGER, Livre en préparation.
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