Displaying similar documents to “Order of holonomy and geometric objects of manifolds with connection”

On prolongation of higher order connections

Miroslav Doupovec, Włodzimierz M. Mikulski (2011)

Annales Polonici Mathematici


We describe all bundle functors G admitting natural operators transforming rth order holonomic connections on a fibered manifold Y → M into rth order holonomic connections on GY → M. For second order holonomic connections we classify all such natural operators.

The vertical prolongation of the projectable connections

Anna Bednarska (2012)

Annales UMCS, Mathematica


We prove that any first order F2 Mm1,m2,n1,n2-natural operator transforming projectable general connections on an (m1,m2, n1, n2)-dimensional fibred-fibred manifold p = (p, p) : (pY : Y → Y) → (pM : M → M) into general connections on the vertical prolongation V Y → M of p: Y → M is the restriction of the (rather well-known) vertical prolongation operator V lifting general connections Γ on a fibred manifold Y → M into VΓ (the vertical prolongation of Γ) on V Y → M.