Abstract
Let p: X → V be a smooth fiber bundle, fiber dimension q, over an n-dimensional manifold V. Let τ ⊂ T(V) be a codimension 1 hyperplane field on V (dim τ = n - 1). Recall the smooth affine bundle of jet spaces \(p_{r - 1}^r :X^{\left( r \right)} \to X^{\left( {r - 1} \right)} ,r \geqslant 1.\) Associated to the hyperplane field τ is a manifold X⊥ and a natural affine R qbundle \(p_ \bot ^r:{X^{\left( r \right)}} \to {X^ \bot }\) defined below, whose local structure provides the natural geometrical setting for applications of the main analytic approximation results of Chapter III, in particular the C⊥-Approximation Theorem 3.8. This bundle “factors” the affine bundle \(p_{r - 1}^r:X\left( r \right) \to {X^{\left( {r - 1} \right)}}\) in the following sense. There is a natural affine bundle \(p_{r - 1}^ \bot :{X^ \bot } \to {X^{\left( {r - 1} \right)}}\) such that,
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© 1998 Springer Basel AG
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Spring, D. (1998). The Geometry of Jet Spaces. In: Convex Integration Theory. Monographs in Mathematics, vol 92. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8940-7_6
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DOI: https://doi.org/10.1007/978-3-0348-8940-7_6
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9836-2
Online ISBN: 978-3-0348-8940-7
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