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Structure d'un drapeau Riemannien complet

Volume 7, Number 2 (2008)

Structure d'un drapeau Riemannien complet

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Abstract

We show that any complete flag on a Riemannian manifold whose metric is bundle-like for any foliation of this flag has its foliations which are transversally paralleli-zable, transversally integrable, and developable on the universal covering of the manifold. Moreover we establish that any stable complete Riemannian flag on a compact manifold is conjuguated to a Lie flag (see definitions). This result is a step toward the classification of Riemannian flags.