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Demonstratio Mathematica
2004 Vol. 37, nr 3 697--707
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 prop[...]
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Demonstratio Mathematica
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Demonstratio Mathematica
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Demonstratio Mathematica
2004 Vol. 37, nr 3 709--717
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Demonstratio Mathematica
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Demonstratio Mathematica
2005 Vol. 38, nr 1 235--238
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.
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Demonstratio Mathematica
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Demonstratio Mathematica
2004 Vol. 37, nr 2 447--462
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Demonstratio Mathematica
2004 Vol. 37, nr 4 963--975
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 canonicall[...]
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Demonstratio Mathematica
EN Natural bundles admitting natural lifting of linear connections are characterized. Corollaries are presented. Some other similar results are obtained, too.
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Demonstratio Mathematica
EN We correct the mistake in the proof of Lemma 7 in our paper "Horizontal extension of connections into (2)-connections" published in Demonstratio Math. XXXVII (4) (2004).
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Demonstratio Mathematica
2005 Vol. 38, nr 4 961--964
EN It is known a complete description of all bundle functors on Mfm x Mf of finite order in the first factor. The most known example of such a bundle functor is the r-jet bundle functor Jr on Mfm x Mf. In the present note an example of a bundle functor on Mfm x Mf of (essentially) infinite order in the[...]
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Demonstratio Mathematica
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.
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Demonstratio Mathematica
EN For natural numbers n > 2 and r > 1 all natural operators T* (Jr(*2T*)) lifting vector fields from n-manifolds M into 1-forms on Jr(*2T*) are classified. It's proved that the set of all natural operators A.
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Demonstratio Mathematica
EN Let m and n be natural numbers. For an arbitrary bundle functor G on the category FMm,n of fibred manifolds with m-dimensional bases and n-dimensional fibers and their local fibered diffeomorphisms we prove that there is no FMm,n-natural operator V transforming general connections.
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Demonstratio Mathematica
EN We define the concept of a fibered fibered (k1, k2, l1, l2)- contact element of order (r1, . . . , r8) for r8 > r4 < r5 > r3, r8 > r6 < r7 > r2 and r1 < ri for ri = 2, 3, . . . , 8. For k1 < m1, k2 < m2, l1 < n1, l2 < n2, we define a bundle func tor Kr1,...,r8/ k1,k2,l1,l2 defined on the category F[...]
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Demonstratio Mathematica
EN Let F : FMm &rarr FM be a bundle functor. We describe all FMm,n- natural operators L transforming functions f : Y &rarr R, Y is an element of Obj(FMm,n), into functions L(f) : FY &rarr R.
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Demonstratio Mathematica
2005 Vol. 38, nr 3 753--760
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.
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