Bundles with spherical Euler class.
In this note, the authors show that the holonomy group of a Riemannian connection on a \(k\)-dimenional Euclidean vector bundle acts transitively on the unit sphere bundle whenever the Euler class is spherical. They give topological criteria when this actually happens and some rigidity consequences for complete, noncompact manifolds of nonnegative sectional curvature. The article is closely related to former work of the first and the last author [see \textit{L. Guijarro, G. Walschap}, Math. Z. 237, No. 2, 251--257 (2001; Zbl 0988.53023)].
scientific article; zbMATH DE number 2101027