Connection, Curvature, and Holonomy for Ehresmann Connections on Riemannian Submersions
We study Ehresmann connections on smooth fibered manifolds equipped with Riemannian submersion structures π: M → Z, focusing on the interaction between horizontal transport and the induced metric geometry on the base manifold. Assuming Riemannian metrics on both the total space and the base, we analyze conditions unde...