Lie derivatives and natural operators
On the natural operators transforming vector fields to the -th tensor power
On cotangent bundles of some natural bundles
The author studies relations between the following two types of natural operators: 1. Natural operators transforming vector fields on manifolds into vector fields on a natural bundle ; 2. Natural operators transforming vector fields on manifolds into functions on the cotangent bundle of . It is deduced that under certain assumptions on , all natural operators of the second type can be constructed through those of the first one.
100th anniversary of birthday of Eduard Čech
On holonomicity criteria in second order geometry.
Prolongation of vector fields to jet bundles
[For the entire collection see Zbl 0699.00032.] In this interesting paper the authors show that all natural operators transforming every projectable vector field on a fibered manifold Y into a vector field on its r-th prolongation are the constant multiples of the flow operator. Then they deduce an analogous result for the natural operators transforming every vector field on a manifold M into a vector field on any bundle of contact elements over M.
Natural operations with second order jets
On the geometric functors on manifolds
On the second order absolute differentiation
In this paper the authors compare two different approaches to the second order absolute differentiation of a fibered manifold (one of them was studied by the authors [Arch. Math., Brno 33, 23-35 (1997; Zbl 0910.53014)]. The main goal is the extension of one approach to connections on functional bundles of all smooth maps between the fibers of two fibered manifolds over the same base (we refer to the book “Natural Operations in Differential Geometry” [Springer, Berlin (1993; Zbl 0782.53013)] and...
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.
Professor Karel Svoboda (1918--1997).
Natural lifting of connections to vertical bundles
One studies the flow prolongation of projectable vector fields with respect to a bundle functor of order on the category of fibered manifolds. As a result, one constructs an operator transforming connections on a fibered manifold into connections on an arbitrary vertical bundle over . It is deduced that this operator is the only natural one of finite order and one presents a condition on vertical bundles over under which every natural operator in question has finite order.
General structured bundles
Summary: [For the entire collection see Zbl 0742.00067.]A general theory of fibre bundles structured by an arbitrary differential-geometric category is presented. It is proved that the structured bundles of finite type coincide with the classical associated bundles.
All natural concomitants of vector valued differential forms
Lie derivatives of sectorform fields
Higher order absolute differentiation with respect to generalized connections
On the torsion of linear higher order connections
For a linear r-th order connection on the tangent bundle we characterize geometrically its integrability in the sense of the theory of higher order G-structures. Our main tool is a bijection between these connections and the principal connections on the r-th order frame bundle and the comparison of the torsions under both approaches.
On the reducibility of connections on the prolongations of vector bundles
Higher order torsions of spaces with Cartan connection
On special types of nonholonomic jets
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