We study the geometry of Riemannian manifolds of finite dimension which are isometric to a quotient of a compact Lie group endowed with the quotient of a bi-invariant metric. Then, we apply the results obtained to enlight the geometry of flag manifolds.By the preceding equivalences, (2.3) yields the decomposition of QQ * Ω into its vertical and horizontal parts in T QQ G, which concludes the proof.

In this paper we present a conditional principle of Gibbs type for independent nonidentically distributed random vectors. We obtain this result by performing Edgeworth expansions for densities of sums of independent random vectors.

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