Riemannian foliations of bounded geometry (Q2929420)

A Riemannian foliation \(\mathcal{F}\) of a Riemannian manifold \((N, g)\) is said to have \textit{bounded geometry} whenever the norms of all the covariant derivatives of the curvature tensor \(R\) and of the O'Neill tensors \(T\) and \(A\) are bounded on \(N\). It is shown that then (1) all the leaves of \(\mathcal{F}\) have bounded geometry in the usual sense, (2) \(N\) can be covered by normal foliation charts for which the coordinates of the Riemannian tensor \(g\) lie in a bounded subset of the Fréchet space of the \(C^\infty\)-functions.