Structure of a complete Riemannian flag (Q1038580)

The author gives a structure theorem for complete Riemannian flags, and he characterizes homogeneous Lie foliation flags on compact connected manifolds. The main result states that for a complete flag on a Riemannian manifold whose metric is bundle-like for any foliation, foliations are transversally parallelizable and transversally integrable. Besides, when the metric is complete, the flag is developable on the universal covering of the manifold.