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Demonstratio Mathematica
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.
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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
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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Demonstratio Mathematica
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Demonstratio Mathematica
EN We present a very simple proof of a general reduction for natural operators on torsion free projectable classical linear connections.
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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
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 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).
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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
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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