Displaying similar documents to “Higher order absolute differentiation with respect to generalized connections”

The vertical prolongation of the projectable connections

Anna Bednarska (2012)

Annales UMCS, Mathematica

Similarity:

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.

On third order semiholonomic prolongation of a connection

Petr Vašík (2011)

Banach Center Publications

Similarity:

We recall several different definitions of semiholonomic jet prolongations of a fibered manifold and use them to derive some interesting properties of prolongation of a first order connection to a third order semiholonomic connection.

Reduction theorem for general connections

Josef Janyška (2011)

Annales Polonici Mathematici

Similarity:

We prove the (first) reduction theorem for general and classical connections, i.e. we prove that any natural operator of a general connection Γ on a fibered manifold and a classical connection Λ on the base manifold can be expressed as a zero order operator of the curvature tensors of Γ and Λ and their appropriate derivatives.

On prolongation of higher order connections

Miroslav Doupovec, Włodzimierz M. Mikulski (2011)

Annales Polonici Mathematici

Similarity:

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.

On iteration of higher order jets and prolongation of connections

Miroslav Doupovec, Włodzimierz M. Mikulski (2011)

Annales Polonici Mathematici

Similarity:

We introduce exchange natural equivalences of iterated nonholonomic, holonomic and semiholonomic jet functors, depending on a classical linear connection on the base manifold. We also classify some natural transformations of this type. As an application we introduce prolongation of higher order connections to jet bundles.