ON JET LIKE  BUNDLES OF VECTOR BUNDLES

M. Doupovec; J. Kurek; W. M. Mikulski

Authors

M. Doupovec Institute of Mathematics, Brno University of Technology, Technická 2, 61669 Brno, Czech Republic Author
J. Kurek Institute of Mathematics, Maria Curie Sklodowska University, pl. Marii Curie Sklodowskiej 1, Lublin, Poland Author
W. M. Mikulski Institute of Mathematics, Jagiellonian University, Lojasiewicza 6, Kraków, Poland Author

Keywords:

Bundle functor, gauge bundle functor, natural transformation, (gauge) natural operator, vector bundle,

Subjects:

58A05, 58A20, 58A32

Abstract

We describe completely the so called jet likefunctors of a vector bundle $E$ over an $m$ -dimensional manifold $M$ ,i.e.\ bundles $F E$ over $M$ canonically depending on $E$ such that $F (E_{1} \times_{M} E_{2}) = F E_{1} \times_{M} F E_{2}$ for any vector bundles $E_{1}$ and $E_{2}$ over $M$ . Then we study how a linear vector field on $E$ can induce canonically a vector field on $F E$ .

ON JET LIKE BUNDLES OF VECTOR BUNDLES

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