Natural relations between connections in 2-fibred manifolds

  • Miroslav Doupovec
  • Alexandr Vondra
Part of the Mathematics and Its Applications book series (MAIA, volume 350)


In the paper, a new approach to the study of interrelations between connections within the framework of a general 2-fibred manifold is introduced. The role of a naturality of the constructions is discussed and the formalism is applied in two particular situations. First, natural relations between connections in J 1 Y→ Y → X are studied and their role for the integrability of partial differential equations represented by connections in question is described. Secondly, the 2-fibred manifold VY → Y → X is investigated. In this case, the importance for a description of the symmetries of equations under consideration is pointed out.


Vector Bundle Natural Transformation Natural Relation Linear Connection Natural Operation 
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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Miroslav Doupovec
    • 1
  • Alexandr Vondra
    • 2
  1. 1.Department of MathematicsTechnical University of BrnoBrnoCzech Republic
  2. 2.Department of MathematicsMilitary Academy in BrnoBrnoCzech Republic

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