Horizontal lifts of tensor fields and connections to the tangent bundle of higher order
Natural affinors on the extended -th order tangent bundles
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.
Horizontal lift of tensor fields of type (1,1) from a manifold to its tangent bundle of higher order
Properties of product preserving functors
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...
Liftings of functions and vector fields to natural bundles
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....
Connexions linéaires conjuguées
Connections of order r
Mixed covariant derivative and conjugate connections
Spaces with a covariant constant linear geometric object
Some vector subbundles of a cotangent bundle of order 2
Some Gauge Natural Operators on Linear Connections.
Relèvements horizontaux de tenseurs de type (1,1) au fibré E = TM⊗T* M
Relèvement horizontal des connexions linéaires au fibré vectoriel associé avec le fibré principal des repères linéaires
Lifts of 1-forms to the tangent bundle of higher order
The tangent bundle of -velocities over a homogeneous space
Connections of higher order and product preserving functors
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.
Page 1