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Comptes Rendus Mathématique
Volume 344, n° 8
pages 503-508 (avril 2007)
Doi : 10.1016/j.crma.2007.03.009
Received : 12 April 2006 ;  accepted : 9 February 2007
Local rigidity of restrictions of Weyl chamber flows
Rigidite locale des restrictions de flots des chambres de Weyl
 

Danijela Damjanović a , Anatole Katok b
a Institut des hautes études scientifiques, 35, route de Chartres, 91440 Bures-sur-Yvette, France 
b Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA 

Abstract

In this Note we consider examples of partially hyperbolic actions: restrictions of Weyl chamber flows on   ( ). We show that generic restrictions of rank at least two are locally rigid. Our approach combines the geometry of the invariant foliations for the action and the algebraic properties of the group  . The method is applicable to restrictions of Weyl chamber flows on other homogeneous spaces. To cite this article: D. Damjanović, A. Katok, C. R. Acad. Sci. Paris, Ser. I 344 (2007).

The full text of this article is available in PDF format.
Résumé

Dans cette Note on étudie des exemples dʼactions partiellement hyperboliques : restrictions de flots des chambres de Weyl sur la variété   ( ). Nous démontrons que, génériquement, les restrictions de rang ≥ 2 sont localement rigides. Notre approche combine la géométrie des feuilletages invariants et les propriétés algébriques du groupe  . Cette approche est aussi applicable dans la démonstration de la rigidité locale des restrictions des autres flots des chambres de Weyl. Pour citer cet article : D. Damjanović, A. Katok, C. R. Acad. Sci. Paris, Ser. I 344 (2007).

The full text of this article is available in PDF format.


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