Hi,

i am have this following problem: suppose B a Riemannian manifold with a metric g, and [O(TB) = \{ p:{\mathbb{R}^k} \to TB,linear{\text{ }}isometries\}][/TEX]
such that TB is isomorphic to O(TB)xR^k, O(TB) principal bundle. Show that ANY metric connection on TB come from a Unique Ehresman connection on O(TB)

Many thanks

W