Abstract

In this note, we show that the holonomy group of a Riemannian connection on a k-dimensional Euclidean vector bundle is transitive on the unit sphere bundle whenever the Euler class χ is spherical. We extract several consequences from this, among them that this is always the case as long as χ does not vanish, and the base of the bundle is simply connected and rationally (k + 1) ∕ 2-connected.

Authors