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Natural affinors on the extended $r$ -th order tangent bundles

Gancarzewicz, Jacek; Kolář, Ivan — 1993

Proceedings of the Winter School "Geometry and Physics"

The authors prove that all natural affinors (i.e. tensor fields of type (1,1) on the extended $r$ -th order tangent bundle $E^{r} M$ over a manifold $M$ ) are linear combinations (the coefficients of which are smooth functions on $ℛ$ ) of four natural affinors defined in this work.

Horizontal lifts of tensor fields and connections to the tangent bundle of higher order

Gancarzewicz, Jacek; Salgado, Modesto — 1989

Proceedings of the Winter School "Geometry and Physics"

Horizontal lift of tensor fields of type (1,1) from a manifold to its tangent bundle of higher order

Gancarzewicz, Jacek; Mahi, Salima; Rahmani, Noureddine — 1987

Proceedings of the 14th Winter School on Abstract Analysis

Properties of product preserving functors

Gancarzewicz, Jacek; Mikulski, Włodzimierz; Pogoda, Zdzisław — 1994

Proceedings of the Winter School "Geometry and Physics"

A product preserving functor is a covariant functor $ℱ$ 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: $ℱ (M_{1} \times M_{2}) = ℱ (M_{1}) \times ℱ (M_{2})$ . It is known that any product preserving functor $ℱ$ is equivalent to a Weil functor $T^{A}$ . Here $T^{A} (M)$ is the set of equivalence classes of smooth maps $ϕ : ℝ^{n} \to M$ and $ϕ, ϕ^{'}$ are equivalent if and only if for every smooth function $f : M \to ℝ$ the formal Taylor series at 0 of $f \circ ϕ$ and $f \circ ϕ^{'}$ are equal in $A = ℝ [[x_{1}, \dots, x_{n}]] / 𝔞$ . In this paper all...

Liftings of functions and vector fields to natural bundles

Jacek Gancarzewicz — 1983

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

Jacek Gancarzewicz — 1973

Annales Polonici Mathematici

Connections of order r

Jacek Gancarzewicz — 1977

Annales Polonici Mathematici

Mixed covariant derivative and conjugate connections

Jacek Gancarzewicz — 1976

Annales Polonici Mathematici

Spaces with a covariant constant linear geometric object

Jacek Gancarzewicz — 1980

Annales Polonici Mathematici

Some vector subbundles of a cotangent bundle of order 2

Jacek Gancarzewicz — 1983

Annales Polonici Mathematici

Some Gauge Natural Operators on Linear Connections.

Jacek Gancarzewicz; Ivan Kolár — 1991

Monatshefte für Mathematik

Relèvements horizontaux de tenseurs de type (1,1) au fibré E = TM⊗T* M

Jacek Gancarzewicz; Naureddine Rahmani — 1988

Annales Polonici Mathematici

Relèvement horizontal des connexions linéaires au fibré vectoriel associé avec le fibré principal des repères linéaires

Jacek Gancarzewicz; Naureddine Rahmani — 1988

Annales Polonici Mathematici

Lifts of 1-forms to the tangent bundle of higher order

Jacek Gancarzewicz; Salima Mahi — 1990

Czechoslovak Mathematical Journal

The tangent bundle of $p^{r}$ -velocities over a homogeneous space

Jacek Gancarzewicz; Modesto R. Salgado — 1991

Czechoslovak Mathematical Journal

Connections of higher order and product preserving functors

Jacek Gancarzewicz; Noureddine Rahmani; Modesto R. Salgado — 2002

Czechoslovak Mathematical Journal

In this paper we consider a product preserving functor $ℱ$ of order $r$ and a connection $Γ$ of order $r$ on a manifold $M$ . We introduce horizontal lifts of tensor fields and linear connections from $M$ to $ℱ (M)$ with respect to $Γ$ . Our definitions and results generalize the particular cases of the tangent bundle and the tangent bundle of higher order.

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Currently displaying 1 – 16 of 16

Natural affinors on the extended $r$ -th order tangent bundles

Horizontal lifts of tensor fields and connections to the tangent bundle of higher order

Horizontal lift of tensor fields of type (1,1) from a manifold to its tangent bundle of higher order

Properties of product preserving functors

Liftings of functions and vector fields to natural bundles

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 $p^{r}$ -velocities over a homogeneous space

Connections of higher order and product preserving functors