Czechoslovak Mathematical Journal

, Volume 62, Issue 2, pp 487–494 | Cite as

On the Weilian prolongations of natural bundles

  • Ivan Kolář


We characterize Weilian prolongations of natural bundles from the viewpoint of certain recent general results. First we describe the iteration F(EM) of two natural bundles E and F. Then we discuss the Weilian prolongation of an arbitrary associated bundle. These two auxiliary results enables us to solve our original problem.


Weil algebra Weil functor natural bundle gauge natural bundle 

MSC 2010

58A20 58A32 


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  1. [1]
    I. Kolář: Weil Bundles as Generalized Jet Spaces. Handbook of Global Analysis, Elsevier, Amsterdam, 2008, pp. 625–664.Google Scholar
  2. [2]
    I. Kolář, P.W. Michor, J. Slovák: Natural Operations in Differential Geometry. Berlin: Springer Verlag, 1993.MATHGoogle Scholar
  3. [3]
    I. Kolář, W. M. Mikulski: On the fiber product preserving bundle functors. Differ. Geom. Appl. 11 (1999), 105–115.MATHCrossRefGoogle Scholar
  4. [4]
    A. Nijenhuis: Natural bundles and their general properties. Geometric objects revisited. Diff. Geometry, in Honor of Kentaro Yano (1972), 317–334.Google Scholar
  5. [5]
    A. Weil: Théorie des points proches sur les variétés différentiables. Colloques internat. Centre nat. Rech. Sci. 52 (1953), 111–117. (In French.)MathSciNetGoogle Scholar

Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2012

Authors and Affiliations

  1. 1.Institute of Mathematics and StatisticsMasaryk UniversityBrnoCzech Republic

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