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1998 | 68 | 2 | 97-106
Tytuł artykułu

The Frölicher-Nijenhuis bracket on some functional spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Two fiber bundles E₁ and E₂ over the same base space M yield the fibered set ℱ(E₁,E₂) → M, whose fibers are defined as $C^{∞}(E₁ₓ,E₂ₓ)$, for each x ∈ M. This fibered set can be regarded as a smooth space in the sense of Frölicher and we construct its tangent prolongation. Then we extend the Frölicher-Nijenhuis bracket to projectable tangent valued forms on ℱ(E₁,E₂). These forms turn out to be a kind of differential operators. In particular, we consider a general connection on ℱ(E₁,E₂) and study the associated covariant differential and curvature.
Rocznik
Tom
68
Numer
2
Strony
97-106
Opis fizyczny
Daty
wydano
1998
otrzymano
1994-06-11
Twórcy
autor
  • Department of Mathematics, Masaryk University, Janáčkovo Nám. 2a, 662 95 Brno, Czech Republic
  • Department of Applied Mathematics "G. Sansone", Via S. Marta 3, 50139 Florence, Italy
Bibliografia
  • [1] A. Cabras and I. Kolář, Connections on some functional bundles, to appear.
  • [2] A. Frölicher, Smooth structures, in: Category Theory 1981, Lecture Notes in Math. 962, Springer, 1982, 69-81.
  • [3] A. Frölicher and A. Nijenhuis, Theory of vector valued differential forms, I, Indag. Math. 18 (1956), 338-359.
  • [4] A. Jadczyk and M. Modugno, An outline of a new geometrical approach to Galilei general relativistic quantum mechanics, to appear.
  • [5] A. Jadczyk and M. Modugno, Galilei general relativistic quantum mechanics, preprint 1993, 1-220.
  • [6] I. Kolář, On the second tangent bundle and generalized Lie derivatives, Tensor (N.S.) 38 (1982), 98-102.
  • [7] I. Kolář, P. Michor and J. Slovák, Natural Operations in Differential Geometry, Springer, 1993.
  • [8] Y. Kosmann-Schwarzbach, Vector fields and generalized vector fields on fibred manifolds, in: Lecture Notes in Math. 792, Springer, 1982, 307-355.
  • [9] L. Mangiarotti and M. Modugno, Graded Lie algebras and connections on fibred spaces, J. Math. Pures Appl. 83 (1984), 111-120.
  • [10] P. Michor, Gauge Theory for Fiber Bundles, Bibliopolis, Napoli, 1991.
  • [11] A. Vanžurová, On geometry of the third order tangent bundle, Acta Univ. Palack. Olomuc. Math. 24 (1985), 81-96.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv68z2p97bwm
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