CONTENTS0. Introduction...................................................................................................51. Natural bundles...........................................................................................102. Liftings of functions.....................................................................................153. Liftings of functions to the r-frame bundle...................................................224. A space of liftings of functions.....................................................................265....
In this paper we consider a product preserving functor of order and a connection of order on a manifold . We introduce horizontal lifts of tensor fields and linear connections from to with respect to . Our definitions and results generalize the particular cases of the tangent bundle and the tangent bundle of higher order.
The authors prove that all natural affinors (i.e. tensor fields of type (1,1) on the extended -th order tangent bundle over a manifold ) are linear combinations (the coefficients of which are smooth functions on ) of four natural affinors defined in this work.
A product preserving functor is a covariant functor from the category of all manifolds and smooth mappings into the category of fibered manifolds satisfying a list of axioms the main of which is product preserving: . It is known that any product preserving functor is equivalent to a Weil functor . Here is the set of equivalence classes of smooth maps and are equivalent if and only if for every smooth function the formal Taylor series at 0 of and are equal in . In this paper all...
Download Results (CSV)