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Erschienen in:
2015 | OriginalPaper | Buchkapitel
1. Jet Prolongations of Fibered Manifolds
verfasst von : Demeter Krupka
Erschienen in: Introduction to Global Variational Geometry
Verlag: Atlantis Press
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Abstract
This chapter introduces fibered manifolds and their jet prolongations. First, we recall properties of differentiable mappings of constant rank and introduce, with the help of rank, the notion of a fibered manifold. Then, we define automorphisms of fibered manifolds as the mappings preserving their fibered structure. The r-jets of sections of a fibered manifold Y, with a fixed positive integer r, constitute a new fibered manifold, the r-jet prolongation
\( J^{r} Y \) of Y; we describe the structure of \( J^{r} Y \) and a canonical construction of automorphisms of \( J^{r} Y \) from automorphisms of the fibered manifold Y, their r-jet prolongation. The prolongation procedure immediately extends, via flows, to vector fields.