Compact finite type foliations
A foliation \(\mathcal F\) on a manifold~\(M\) is Riemannian if there exists a Riemannian metric on~\(M\) for which the leaves of~\(\mathcal F\) are equidistant. Such foliations have especially nice properties. For this reason, one is interested in finding sufficient conditions for a foliation to be Riemannian. In this paper, the author looks at the lift of a foliation~\(\mathcal F\) to a foliation \({\mathcal F}^r\) of the same dimension on the bundle of transverse \(r\)-jets to~\(\mathcal F\). He shows that \(\mathcal F\) is Riemannian if, for some~\(r\), \({\mathcal F}^r\) is transversely parallelizable and has relatively compact leaves.
scientific article; zbMATH DE number 2094048