NDLI: On symmetrization of jets

Content Provider	Springer Nature Link
Author	Mikulski, W. M.
Copyright Year	2011
Abstract	Let F = F (A,H,t) and $${F^1} = {F^{({A^1},{H^1},{t^1})}}$$ be fiber product preserving bundle functors on the category FM m of fibred manifolds Y with m-dimensional bases and fibred maps covering local diffeomorphisms. We define a quasi-morphism (A, H, t) → (A 1, H 1, t 1) to be a GL(m)-invariant algebra homomorphism ν: A → A 1 with t 1 = ν ∘ t. The main result is that there exists an FM m -natural transformation FY → F 1 Y depending on a classical linear connection on the base of Y if and only if there exists a quasi-morphism (A, H, t) → (A 1, H 1, t 1). As applications, we study existence problems of symmetrization (holonomization) of higher order jets and of holonomic prolongation of general connections.
Ending Page	168
Page Count	12
Starting Page	157
File Format	PDF
ISSN	00114642
e-ISSN	15729141
Journal	Czechoslovak Mathematical Journal
Issue Number	1
Volume Number	61
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-03-18
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	natural operators bundle functors Mathematics jets Weil functors Ehresmann prolongation Differentiable manifolds, foundations Natural bundles Ordinary Differential Equations Analysis Convex and Discrete Geometry Jets Mathematical Modeling and Industrial Mathematics higher order connections
Content Type	Text
Resource Type	Article
Subject	Mathematics

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On symmetrization of jets