## 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.

### MSC:

 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
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### References:

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