Geometriae Dedicata

, Volume 112, Issue 1, pp 141–164 | Cite as

Une Dualité Pour Les Courbes Hyperconvexes

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Abstract

An hyperconvex curve is a curve ξ1 in \(\mathbb{P}(\mathbb{R}^{n})\) such that any n distinct points of the curve are in direct sum. We give here a property of duality of those curves when they admit furthermore an osculating flag. Namely if \((\xi^{1}, \ldots, \xi^{n-1})\) is a continuous curve of osculating flags of an hyperconvex curve ξ1, we prove that the curve ξn-1 is hyperconvex too and admit a curve of osculating flags.

Keywords

Cayley graphs quasi-isometry symmetric space 

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References

  1. 1.
    Kuiper N.H. On convex locally-projective spaces. In: Convegno Internazionale di Geometric, Differen-ziale, Italia, 1953, p. 200–213. Edizioni Cremonese, Roma, 1954Google Scholar
  2. 2.
    Labourie F. Anosov flows, surface groups and curves in projective space, pre-print, 2003Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.DMA, ENSParisFrance

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