Geometriae Dedicata

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

Une Dualité Pour Les Courbes Hyperconvexes



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.


Cayley graphs quasi-isometry symmetric space 


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    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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