General Mathematics, Vol. 5, No. 1 - 4, pp. 237-246, 1995

E. Macias Virgos -- The Diffeomorphism Group of a Riemannian Foliation

Abstract: We present without proofs some recent results on Riemannian foliations. First we consider the (infinite dimensional) manifold ${\cal M}(M/F)$ of bundle-like metrics on a foliated manifold $(M,F)$. Then we show how to construct an adapted local addition for any Riemannian foliation. Also the notion of foliate vector field along a map is introduced. This allows us to endow the space ${\rm Diff}(M/F)$ of foliation preserving diffeomorphisms with a manifold structure. Finally, we study the group of transverse isometries of a Lie foliation in the setting of $Q$-manifolds.

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