Lifting of a Riemannian flag and Lie flags of the \(n+1\)-dimensional hyperbolic torus. (Relèvement d’un drapeau riemannien et drapeaux de Lie du tore hyperbolique \(n+1\)-dimensionnel.) (French) Zbl 1096.53032

The author shows that any flag of Riemannian foliations on a compact connected orientable Riemannian manifold lifts on the bundle of transverse direct orthonormal frames to a flag of transversally parallelizable foliations. This result permits to obtain a classification of \((n+ 1)\)-dimensional compact orientable Riemannian manifolds for which the dimension of the structural Lie algebra of the flow is equal to \(n\) or \(n-1\).


53C40 Global submanifolds
53C12 Foliations (differential geometric aspects)
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