Smooth bundles of generalized half-densities

Daniel Canarutto

Archivum Mathematicum (2000)

  • Volume: 036, Issue: 2, page 111-124
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Canarutto, Daniel. "Smooth bundles of generalized half-densities." Archivum Mathematicum 036.2 (2000): 111-124. <http://eudml.org/doc/248575>.

@article{Canarutto2000,
abstract = {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.},
author = {Canarutto, Daniel},
journal = {Archivum Mathematicum},
keywords = {generalized sections; Frölicher smoothness; connections; generalized sections; Frölicher smoothness; connections},
language = {eng},
number = {2},
pages = {111-124},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Smooth bundles of generalized half-densities},
url = {http://eudml.org/doc/248575},
volume = {036},
year = {2000},
}

TY - JOUR
AU - Canarutto, Daniel
TI - Smooth bundles of generalized half-densities
JO - Archivum Mathematicum
PY - 2000
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 036
IS - 2
SP - 111
EP - 124
AB - 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.
LA - eng
KW - generalized sections; Frölicher smoothness; connections; generalized sections; Frölicher smoothness; connections
UR - http://eudml.org/doc/248575
ER -

References

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  8. Kriegl A., Michor P., The convenient setting of global analysis, American Mathematical Society 1997. (1997) Zbl0889.58001MR1471480
  9. Kolář I., Michor P., Slovák J., Natural Operations in Differential Geometry, Springer-Verlag 1993. (1993) MR1202431
  10. Modugno M., Kolář I., The Frölicher-Nijenhuis bracket on some functional spaces, Ann. Pol. Math. LXVIII.2 (1998), 97–106. (1998) Zbl0982.53024MR1610540
  11. Mangiarotti L., Modugno M., Graded Lie algebras and connections on fibred spaces, J. Math. Pures Appl. 83 (1984), 111–120. (1984) MR0776913
  12. Schwartz L., Théorie des distributions, Hermann, Paris 1966. (1966) Zbl0149.09501MR0209834
  13. Slovák J., Smooth structures on fibre jet spaces, Czech. Math. J. 36, 111 (1986), 358–375. (1986) MR0847766

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