On the relation between connection and sprays

A well-known (and simple) result of linear algebra asserts that any bilinear symmetric form RnxR→ δ Rn is completely determined by its values on the diagonal: letting σ (t) = δ (t,t) be the quadratic form associated to δ, we may recover the original form δ simply as the polar form of σ, i.e. δ (t1,t...