Lagrangians and Euler morphisms on fibered-fibered frame bundles from projectable-projectable classical linear connections

Lagrangians and Euler morphisms on fibered - fibered frame bundles from projectable - projectable classical linear connections

We classify all FMm1,m2,n1,n2 -natural operators A transforming projectable-projectable torsion-free classical linear connections ∇ on fibered-fibered manifolds Y of dimension (m1,m2, n1, n2) into rth order Lagrangians A(∇) on the fibered-fibered linear frame bundle L(Y ) on Y . Moreover, we classify all FMm1,m2,n1,n2 -natural operators B transforming projectable-projectable torsion-free classi...

BEDNARSKA On lifts of projectable - projectable classical linear connections to the cotangent bundle

We describe all FMm1,m2,n1,n2 -natural operators D : Qproj-proj QT ∗ transforming projectable-projectable classical torsion-free linear connections ∇ on fibred-fibred manifolds Y into classical linear connections D(∇) on cotangent bundles T ∗Y of Y . We show that this problem can be reduced to finding FMm1,m2,n1,n2 -natural operators D : Qproj-proj (T ∗,⊗pT ∗⊗⊗qT ) for p = 2, q = 1 and p = 3, q...

Covariant Field Theory on Frame Bundles of Fibered Manifolds †

We show that covariant field theory for sections of π : E → M lifts in a natural way to the bundle of vertically adapted linear frames LπE. Our analysis is based on the fact that LπE is a principal fiber bundle over the bundle of 1-jets J1π. On LπE the canonical soldering 1-forms play the role of the contact structure of J1π. A lifted Lagrangian L:LπE → R is used to construct modified soldering...

From Hyperbolic Polynomials to Real Fibered Morphisms

Constraints on Exact Lagrangians in Cotangent Bundles of Manifolds Fibered over the Circle

We give topological obstructions to the existence of a closed exact Lagrangian submanifold L →֒ T M , where M is the total space of a fibration over the circle. For instance, we show that π1(L) cannot be the free product of two non-trivial groups and that the difference between the number of generators and the number of relations in a finite presentation of π1(L) is less than two. Mathematics su...