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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.

Natural lifting of connections to vertical bundles

Kolář, Ivan, Mikulski, Włodzimierz M. (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

One studies the flow prolongation of projectable vector fields with respect to a bundle functor of order $(r, s, q)$ on the category of fibered manifolds. As a result, one constructs an operator transforming connections on a fibered manifold $Y$ into connections on an arbitrary vertical bundle over $Y$ . It is deduced that this operator is the only natural one of finite order and one presents a condition on vertical bundles over $Y$ under which every natural operator in question has finite order.

Natural liftings of foliations to the $r$ -tangent bunde

Mikulski, Włodzimierz M. (1994)

Proceedings of the Winter School "Geometry and Physics"

Let $F$ be a $p$ -dimensional foliation on an $n$ -manifold $M$ , and $T^{r} M$ the $r$ -tangent bundle of $M$ . The purpose of this paper is to present some reltionship between the foliation $F$ and a natural lifting of $F$ to the bundle $T^{r} M$ . Let $L_{q}^{r} (F)$ $(q = 0,...Natural lifts of classical linear connections to the cotangent bundle Kureš, Miroslav

(1996)

Proceedings of the 15th Winter School "Geometry and Physics"Natural operations of Hamiltonian type on the cotangent bundle Doupovec, Miroslav, Kurek, Jan

(1997)

Proceedings of the 16th Winter School "Geometry and Physics" The authors study some geometrical constructions on the cotangent bundle T^{*} M from the viewpoint of natural operations. First they deduce that all natural operators transforming functions on T^{*} M into vector fields on T^{*} M are linearly generated by the Hamiltonian vector field with respect to the canonical symplectic structure of T^{*} M and by the Liouville vector field of T^{*} M . Then they determine all natural operators transforming pairs of functions on T^{*} M into functions on T^{*} M . In this case, the main generator is...Natural operations with second order jets Kolář, Ivan, Vosmanská, Gabriela

(1987) Proceedings of the 14th Winter School on Abstract AnalysisNatural operators between vector valued differential forms Cap, Andreas

(1991) Proceedings of the Winter School "Geometry and Physics" [For the entire collection see Zbl 0742.00067.]This paper is devoted to a method permitting to determine explicitly all multilinear natural operators between vector-valued differential forms and between sections of several other natural vector bundles.Natural operators lifting functions to cotangent bundles of linear higher order tangent bundles Mikulski, W. M.

(1996) Proceedings of the 15th Winter School "Geometry and Physics" The author studies the problem how a map L : M \to ℝ on an n -dimensional manifold M can induce canonically a map A_{M} (L) : T^{*} T^{(r)} M \to ℝ for r a fixed natural number. He proves the following result: “Let A : T^{(0, 0)} \to T^{(0, 0)} (T^{*} T^{(r)}) be a natural operator for n -manifolds. If n \geq 3 then there exists a uniquely determined smooth map H : ℝ^{S (r)} \times ℝ \to ℝ such that A = A^{(H)} .”The conclusion is that all natural functions on T^{*} T^{(r)} for n -manifolds (n \geq 3) are of the form {H \circ (λ_{M}^{〈 0, 1 〉}, \dots, λ_{M}^{〈 r, 0 〉})}, where H \in C^{\infty} (ℝ^{r}) is a function of r variables.Natural operators lifting vector fields on manifolds to the bundles of covelocities Mikulski, W. M.

(1996) Proceedings of the Winter School "Geometry and Physics" The author proves that for a manifold M of dimension greater than 2 the sets of all natural operators T M \to (T_{k}^{r *} M, T_{ℓ}^{q *} M) and T M \to T T_{k}^{r *} M, respectively, are free finitely generated C^{\infty} ({(ℝ^{k})}^{r}) -modules. The space T_{k}^{r *} M = J^{r} {(M, ℝ^{k})}_{0}, this is, jets with target 0 of maps from M to ℝ^{k}, is called the space of all (k, r) -covelocities on M . Examples of such operators are shown and the bases of the modules are explicitly constructed. The definitions and methods are those of the book of I. Kolář, P. W. Michor and J. Slovák [Natural operations in differential geometry,...Natural operators on frame bundles Krupka, Michal

(2000) Proceedings of the 19th Winter School "Geometry and Physics" Let F_{1} be a natural bundle of order r_{1}; a basis of the s -th order differential operators of F_{1} with values in r_{2} -th order bundles is an operator D of that type such that any other one is obtained by composing D with a suitable zero-order operator. In this article a basis is found in the following two cases: for F_{1} = semi F^{r_{1}} (semi-holonomic r_{1} -th order frame bundle), s = 0, r_{2} < r_{1} and F_{1} = F^{1} (1 -st order frame bundle), r_{2} \leq s . The author uses here the so-called method of orbit reduction which provides one with a criterion for checking...Natural operators on vector fields on the cotangent bundles of the bundles of (k, r) -velocities Tomáš, Jiří

(1998) Proceedings of the 17th Winter School "Geometry and Physics"Natural operators transforming projectable vector fields to product preserving bundles Tomáš, Jiří

(1999) Proceedings of the 18th Winter School "Geometry and Physics" Let Y \to M be a fibered manifold over a manifold M and μ : A \to B be a homomorphism between Weil algebras A and B . Using the results of Mikulski and others, which classify product preserving bundle functors on the category of fibered manifolds, the author classifies all natural operators T_{proj} Y \to T^{μ} Y, where T_{proj} Y denotes the space of projective vector fields on Y and T^{μ} the bundle functors associated with μ .Natural symplectic structures on the tangent bundle of a space-time Janyška, Josef

(1996) Proceedings of the 15th Winter School "Geometry and Physics" In this nice paper the author proves that all natural symplectic forms on the tangent bundle of a pseudo-Riemannian manifold are pull-backs of the canonical symplectic form on the cotangent bundle with respect to some diffeomorphisms which are naturally induced by the metric.Natural transformations of affine connections on manifolds to metrics on cotangent bundles Sekizawa, Masami

(1987) Proceedings of the 14th Winter School on Abstract AnalysisNatural transformations of affinors into functions and affinors Dębecki, Jacek

(1993) Proceedings of the Winter School "Geometry and Physics"Natural transformations of Lagrangians Dębecki, Jacek

(1994) Proceedings of the Winter School "Geometry and Physics"Natural transformations of Weil functors into bundle functors Mikulski, Włodzimierz M.

(1990) Proceedings of the Winter School "Geometry and Physics" [For the entire collection see Zbl 0699.00032.] Natural transformations of the Weil functor T^{A} of A-velocities [I. Kolař, Commentat. Math. Univ. Carol. 27, 723-729 (1986; Zbl 0603.58001)] into an arbitrary bundle functor F are characterized. In the case where F is a linear bundle functor, the author deduces that the dimension of the vector space of all natural transformations of T^{A} into F is finite and is less than or equal to dim (F_{0} ℛ^{k}) . The spaces of all natural transformations of Weil functors into linear...Necessary conditions for local convexifiability of pseudoconvex domains in ℂ^{2} Kolář, Martin

(2002) Proceedings of the 21st Winter School "Geometry and Physics"Necessary conditions for the multiple integral problem and elliptic variational inequalities Barbu, Viorel

(1982) Equadiff 5New boson realizations of quantum groups U_{q} (A_{n}) Burdík, Č., Navrátil, O.

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

Natural lifting of connections to vertical bundles

Natural liftings of foliations to the $r$ -tangent bunde

Natural lifts of classical linear connections to the cotangent bundle

Natural operations of Hamiltonian type on the cotangent bundle

Natural operations with second order jets

Natural operators between vector valued differential forms

Natural operators lifting functions to cotangent bundles of linear higher order tangent bundles

Natural operators lifting vector fields on manifolds to the bundles of covelocities

Natural operators on frame bundles

Natural operators on vector fields on the cotangent bundles of the bundles of $(k, r)$ -velocities

Natural operators transforming projectable vector fields to product preserving bundles

Natural symplectic structures on the tangent bundle of a space-time

Natural transformations of affine connections on manifolds to metrics on cotangent bundles

Natural transformations of affinors into functions and affinors

Natural transformations of Lagrangians

Natural transformations of Weil functors into bundle functors

Necessary conditions for local convexifiability of pseudoconvex domains in $ℂ^{2}$

Necessary conditions for the multiple integral problem and elliptic variational inequalities

New boson realizations of quantum groups $U_{q} (A_{n})$

Currently displaying 1 – 20 of 66