De la caract\'erisation matricielle des drapeaux complets d'extensions riemanniennes aux feuilletages riemanniens transversalement diagonaux sur une vari\'et\'e compacte connexe

Abstract

In this paper we characterise with the matrix the complete flag of riemannian extension (see d\'efinition) on a riemannian compact manifold whose metric is bundlelike for any foliation F_{s} of this flag. This study show us that a foliation of a complete flag of riemannian extension on a riemannian compact manifold whose metric is bundlelike for any foliation of this flag is a transversely diagonal riemannian foliation (see d\'efinition).