A flag on a manifold $M$ is an increasing sequence of foliations $left( mathcal{F}_{1},cdots ,mathcal{F}_{p}ight) $ on this manifold, where for each $i$, $dim mathcal{F}_{i}=i$. The aim of this paper is to etablish that any flag of riemannian foliations $mathcal{D=}$ $left( mathcal{F}_{1},cdots ,mathcal{F}_{p}ight) $ on a compact and connected manifold, lifts on the bundle of transverse direct orthonormal frames of $mathcal{F}_{p}$ to a flag of transversally parallelizable foliations. This result permits us to obtain a classification of riemannian flags of a $n+1$-dimensional compact manifold for which the dimension of the structural Lie algebra of the flow is equal to $n$ or $n-1$.
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机译：流形$ M $上的标志是该流形上的叶子$ left（ mathcal {F} _ {1}， cdots， mathcal {F} _ {p} right）$的递增序列，其中每个$ i $，$ dim mathcal {F} _ {i} = i $。这篇文章的目的是建立任何黎曼叶面标记$ mathcal {D =} $ $ left（ mathcal {F} _ {1}， cdots， mathcal {F} _ {p} right ）$在紧凑且相连的流形上，将$ mathcal {F} _ {p} $的横向正交正交框架束举起，以形成可横向并行化的叶面标志。该结果使我们能够获得维数为nn + 1的紧凑流形的黎曼标志的分类，对于该流形，流的结构李代数的维数等于nn或n-1。
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