Smooth bundles of generalized half-densities
Canarutto, Daniel
Archivum Mathematicum, Tome 036 (2000), p. 111-124 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2000-01-01
Classification:  46F99,  46T30,  53C05,  58B10,  58C99 
@article{107724,
     author = {Daniel Canarutto},
     title = {Smooth bundles of generalized half-densities},
     journal = {Archivum Mathematicum},
     volume = {036},
     year = {2000},
     pages = {111-124},
     zbl = {1050.46515},
     mrnumber = {1761616},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107724}
}

Canarutto, Daniel. Smooth bundles of generalized half-densities. Archivum Mathematicum, Tome 036 (2000) pp. 111-124. http://gdmltest.u-ga.fr/item/107724/

Boman J. Differentiability of a function and of its composition with functions of one variable, Math. Scand. 20 (1967), 249–268. (1967) | MR 0237728

Bogolubov N.N.; Logunov A.A.; Todorov I.T. Introduction to Axiomatic Quantum Field Theory, Benjamin, Reading (1975). (1975) | MR 0452277

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. (1995) | MR 1464298 | Zbl 0851.58007

Frölicher A. Smooth structures, LNM 962, Springer-Verlag 1982, 69–81. (1982) | MR 0682945

Frölicher A.; Kriegl A. Linear spaces and differentiation theory, John Wiley & Sons (1988). (1988) | MR 0961256 | Zbl 0657.46034

Frölicher A.; Nijenhuis A. Theory of vector valued differential forms, I, Indag. Math. 18 (1956), 338–359. (1956) | MR 0082554

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. (1992) | MR 1349843

Kriegl A.; Michor P. The convenient setting of global analysis, American Mathematical Society 1997. (1997) | MR 1471480 | Zbl 0889.58001

Kolář I.; Michor P.; Slovák J. Natural Operations in Differential Geometry, Springer-Verlag 1993. (1993) | MR 1202431

Modugno M.; Kolář I. The Frölicher-Nijenhuis bracket on some functional spaces, Ann. Pol. Math. LXVIII.2 (1998), 97–106. (1998) | MR 1610540 | Zbl 0982.53024

Mangiarotti L.; Modugno M. Graded Lie algebras and connections on fibred spaces, J. Math. Pures Appl. 83 (1984), 111–120. (1984) | MR 0776913

Schwartz L. Théorie des distributions, Hermann, Paris 1966. (1966) | MR 0209834 | Zbl 0149.09501

Slovák J. Smooth structures on fibre jet spaces, Czech. Math. J. 36, 111 (1986), 358–375. (1986) | MR 0847766