HORIZONTAL LIFTS OF PROJECTABLE LINEAR CONNECTION TO SEMI-TANGENT BUNDLE

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...

LIFTINGS OF 1 - FORMS TO THE LINEAR r - TANGENT BUNDLE

Let r; n be xed natural numbers. We prove that for n-manifolds the set of all linear natural operators T ! T T (r) is a nitely dimensional vector space over R. We construct explicitly the bases of the vector spaces. As a corollary we nd all linear natural operators T ! T r. All manifolds and maps are assumed to be innnitely diierentiable. 0. Let r; n be xed natural numbers. Given a manifold M w...

Tangent Lifts of Poisson and Related

Tangent Lifts of Poisson and Related Structures

The derivation d T on the exterior algebra of forms on a manifold M with values in the exterior algebra of forms on the tangent bundle TM is extended to multivector fields. These tangent lifts are studied with applications to the theory of Poisson structures, canonical vector fields and Poisson-Lie groups. 0. Introduction. A derivation d on the exterior algebra of forms on a manifold M with val...

ON THE LIFTS OF SEMI-RIEMANNIAN METRICS

In this paper, we extend Sasaki metric for tangent bundle of a Riemannian manifold and Sasaki-Mok metric for the frame bundle of a Riemannian manifold [I] to the case of a semi-Riemannian vector bundle over a semi- Riemannian manifold. In fact, if E is a semi-Riemannian vector bundle over a semi-Riemannian manifold M, then by using an arbitrary (linear) connection on E, we can make E, as a...