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1
Content available On the twisted Dorfman-Courant like brackets
EN
There are completely described all [formula]-gauge-natural operators C which, like to the Dorfman-Courant bracket, send closed linear 3-forms [formula]on a smooth (C ∞) vector bundle E into R-bilinear operators [formula] transforming pairs of linear sections of [formula] into linear sections of [formula]. Then all such C which also, like to the twisted Dorfman-Courant bracket, satisfy both some “restricted” condition and the Jacobi identity in Leibniz form are extracted.
2
Content available remote Reduction for natural operators on projectable connections
EN
We present a very simple proof of a general reduction for natural operators on torsion free projectable classical linear connections.
3
Content available remote On naturality of the Legendre operator
EN
We deduce that all natural operators of the type of the Legendre operator from the variational calculus in fibred manifolds are the constant multiples of the Legendre operator.
EN
We construct some extension [...] of the flow operator [...] fibred frame bundle functor. Next using operator [...] we present some construction of general connections[...] depending on classical (not necessarily projectable) linear connections V on Y.
5
Content available remote Natural liftings of connections to the r-th order bundle
EN
We describe all natural operators A lifting a clasiccal linear connection on an m-dimensional manifold M into a classical linear conection A() on the r-th order frame bundle LrM = invJr/0 (Rm,M).
6
Content available remote The natural bundles admitting natural lifting of linear connections
EN
Natural bundles admitting natural lifting of linear connections are characterized. Corollaries are presented. Some other similar results are obtained, too.
7
Content available remote The natural operators transforming projectable vector fields to vertical bundles
EN
Let F : Mfn -> FM. be a natural bundle. We classify all FMm,n-natural operators D transforming projectable vector fields X on (m, n)-dimensional fibered manifolds Y - M to vector fields D{X) on the F-vertical bundle VFY -> M. We apply this classification result to some more known natural bundles F.
8
Content available remote On naturality of the formal Euler operator
EN
That all natural operators of the type of formal Euler operator from the variational calculus are the constant multiples of the formal Euler operator is deduced.
EN
For any product-preserving bundle functor F denned on the category F2 M of fibered-fibered manifolds, we determine all natural operators transforming projectable-projectable vector fields on Y 6 Ob(F2M) to vector fields on FY. We also determine all natural affinors on FY and prove a composition property analogous to that concerning Weil bundles.
12
Content available remote Horizontal extension of connections into (2)-connections
EN
We discuss the prolongation of connections to to some non product preserving bundles. We introduce the concept of (r)-connection on a fibered manifold Y and for a given connection F on Y we construct its horizontal extension F(2). We also prove that F(2 ) is the unique (2)-connection on Y canonically dependent on F.
13
Content available remote The natural linear operators Λp T* → TTr*
EN
For integers p ≥ 0, n ≥ p+2 and r ≥ 1 all natural linear operators Λp T*|Mfn → TTr* transforming p-forms from n-manifolds M into vector fields on the r-th order cotangent bundle Tr* M = Jr (M, R)0 of M are completely described.
14
Content available remote On the contact (k, r)-coelements
15
Content available remote On some natural operators in vector fields
16
Content available remote Liftings of vector fields to (JrT*,a)
17
Content available remote 2-forms induced by lagrangians on weil bundles
EN
Let Q : B - A be an algebra epimorphism of Well algebras and let Q :T M -> T M be the canonical extension of Q over a manifold M. The full classification of natural operators transforming functions TAM -"o R into 2-forms on TBM of finite order with respect to Q is given.
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