Geodesic
Smooth bundles of generalized half-densities
Archivum mathematicum, Tome 36 (2000) no. 2, pp. 111-124 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Smooth bundles, whose fibres are distribution spaces, are introduced according to the notion of smoothness due to Frölicher. Some fundamental notions of differential geometry, such as tangent and jet spaces, Frölicher-Nijenhuis bracket, connections and curvature, are suitably generalized. It is also shown that a classical connection on a finite-dimensional bundle naturally determines a connection on an associated distributional bundle.
Smooth bundles, whose fibres are distribution spaces, are introduced according to the notion of smoothness due to Frölicher. Some fundamental notions of differential geometry, such as tangent and jet spaces, Frölicher-Nijenhuis bracket, connections and curvature, are suitably generalized. It is also shown that a classical connection on a finite-dimensional bundle naturally determines a connection on an associated distributional bundle.
Classification : 46F99, 46T30, 53C05, 58B10, 58C99
Keywords: generalized sections; Frölicher smoothness; connections 
@article{ARM_2000_36_2_a3,
     author = {Canarutto, Daniel},
     title = {Smooth bundles of generalized half-densities},
     journal = {Archivum mathematicum},
     pages = {111--124},
     year = {2000},
     volume = {36},
     number = {2},
     mrnumber = {1761616},
     zbl = {1050.46515},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2000_36_2_a3/}
}
TY  - JOUR
AU  - Canarutto, Daniel
TI  - Smooth bundles of generalized half-densities
JO  - Archivum mathematicum
PY  - 2000
SP  - 111
EP  - 124
VL  - 36
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ARM_2000_36_2_a3/
LA  - en
ID  - ARM_2000_36_2_a3
ER  - 
%0 Journal Article
%A Canarutto, Daniel
%T Smooth bundles of generalized half-densities
%J Archivum mathematicum
%D 2000
%P 111-124
%V 36
%N 2
%U http://geodesic.mathdoc.fr/item/ARM_2000_36_2_a3/
%G en
%F ARM_2000_36_2_a3
Canarutto, Daniel. Smooth bundles of generalized half-densities. Archivum mathematicum, Tome 36 (2000) no. 2, pp. 111-124. http://geodesic.mathdoc.fr/item/ARM_2000_36_2_a3/

[Bo67] Boman J.: Differentiability of a function and of its composition with functions of one variable. Math. Scand. 20 (1967), 249–268. | MR

[BLT75] Bogolubov N.N., Logunov A.A., Todorov I.T.: Introduction to Axiomatic Quantum Field Theory. Benjamin, Reading (1975). | MR

[CK] Cabras A., Kolář I., - : Connections on some functional bundles. Czech. Math. J. 45, 120 (1995), 529–548. - On the iterated absolute differentiation on some functional bundles, Arch. Math. Brno 33 (1997), 23–35. - The universal connection of an arbitrary system, Ann. Mat. Pura e Appl. (IV) Vol. CLXXIV (1998), 1–11. | MR | Zbl

[Fr82] Frölicher A.: Smooth structures. LNM 962, Springer-Verlag 1982, 69–81. | MR

[FK88] Frölicher A., Kriegl A.: Linear spaces and differentiation theory. John Wiley & Sons (1988). | MR | Zbl

[FN56] Frölicher A., Nijenhuis A.: Theory of vector valued differential forms, I. Indag. Math. 18 (1956), 338–359. | MR

[JM] Jadczyk A., Modugno M., - : An outline of a new geometrical approach to Galilei general relativistic quantum mechanics. in Proc. XXI Int. Conf. on Differential Geometric Methods in Theoretical Physics, Tianjin 5-9 June 1992, ed. Yang, C.N. et al., pp 543–556, World Scientific, Singapore, 1992. - A scheme for Galilei general relativistic quantum mechanics, in General Relativity and Gravitational Physics, M. Cerdonio, R. D’Auria, M. Francaviglia, G. Magnano eds., World Scientific, Singapore (1994), 319–337. | MR

[KM97] Kriegl A., Michor P.: The convenient setting of global analysis. American Mathematical Society 1997. | MR | Zbl

[KMS93] Kolář I., Michor P., Slovák J.: Natural Operations in Differential Geometry. Springer-Verlag 1993. | MR

[MK98] Modugno M., Kolář I.: The Frölicher-Nijenhuis bracket on some functional spaces. Ann. Pol. Math. LXVIII.2 (1998), 97–106. | MR | Zbl

[MM84] Mangiarotti L., Modugno M.: Graded Lie algebras and connections on fibred spaces. J. Math. Pures Appl. 83 (1984), 111–120. | MR

[Sc66] Schwartz L.: Théorie des distributions. Hermann, Paris 1966. | MR | Zbl

[Sl86] Slovák J.: Smooth structures on fibre jet spaces. Czech. Math. J. 36, 111 (1986), 358–375. | MR