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Natural liftings of $(0, 2)$ -tensor fields to the tangent bundle

Miroslav Doupovec (1994)

Archivum Mathematicum

We determine all first order natural operators transforming $(0, 2)$ –tensor fields on a manifold $M$ into $(0, 2)$ –tensor fields on $T M$ .

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 liftings of foliations to the tangent bundle Włodzimierz M. Mikulski

(1992)

Mathematica Bohemica A classification of natural liftings of foliations to the tangent bundle is given.Natural liftings of vector fields to tangent bundles of bundles of 1 -forms Piotr Kobak

(1991) Mathematica Bohemica Natural liftings D : I \to I T T^{*} are classified for n \geq 2 . It is proved that they form a 5-parameter family of operators.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 in the view of Cartan geometries Martin Panák

(2003) Archivum Mathematicum We prove, that r -th order gauge natural operators on the bundle of Cartan connections with a target in the gauge natural bundles of the order (1, 0) (“tensor bundles”) factorize through the curvature and its invariant derivatives up to order r - 1 . On the course to this result we also prove that the invariant derivations (a generalization of the covariant derivation for Cartan geometries) of the curvature function of a Cartan connection have the tensor character. A modification of the theorem is given for...Natural operators lifting functions to affinors on higher order cotangent bundles W. M. Mikulski

(2004) Annales Polonici Mathematici For natural numbers n \geq 3 and r \geq 1 all natural operators A : T_{| ℳ f ₙ}^{(0, 0)} ⟿ T^{(1, 1)} T^{r *} transforming functions from n-manifolds into affinors (i.e. tensor fields of type (1,1)) on the r-cotangent bundle are classified.Natural operators lifting functions to bundle functors on fibered manifolds Włodzimierz M. Mikulski

(1998) Archivum Mathematicum The complete description of all natural operators lifting real valued functions to bundle functors on fibered manifolds is given. The full collection of all natural operators lifting projectable real valued functions to bundle functors on fibered manifolds is presented.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 lifting vector fields to bundles of Weil contact elements Miroslav Kureš, Włodzimierz M. Mikulski

(2004) Czechoslovak Mathematical Journal Let A be a Weil algebra. The bijection between all natural operators lifting vector fields from m -manifolds to the bundle functor K^{A} of Weil contact elements and the subalgebra of fixed elements S A of the Weil algebra A is determined and the bijection between all natural affinors on K^{A} and S A is deduced. Furthermore, the rigidity of the functor K^{A} is proved. Requisite results about the structure of S A are obtained by a purely algebraic approach, namely the existence of nontrivial S A is discussed.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 projectors in tensor spaces. Krupka, Demeter

(2002) Beiträge zur Algebra und GeometrieNatural pseudodistances between closed surfaces Pietro Donatini, Patrizio Frosini

(2007) Journal of the European Mathematical Society Let us consider two closed surfaces ℳ, 𝒩 of class C^{1} and two functions ϕ : ℳ \to ℝ, ψ : 𝒩 \to ℝ of class C^{1}, called measuring functions. The natural pseudodistance d between the pairs (ℳ,), (𝒩, ψ) is defined as the infimum of Θ (f) : = {max}_{P \in ℳ} | ϕ (P) - ψ (f (P)) | as f varies in the set of all homeomorphisms from ℳ onto 𝒩 . In this paper we prove that the natural pseudodistance equals either | c_{1} - c_{2} |, \frac{1}{2} | c_{1} - c_{2} |, or \frac{1}{3} | c_{1} - c_{2} |, where c_{1} and c_{2} are two suitable critical values of the measuring functions. This shows that a previous relation between the natural
pseudodistance and critical values...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.Currently displaying 21 -
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Natural liftings of $(0, 2)$ -tensor fields to the tangent bundle

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

Natural liftings of foliations to the tangent bundle

Natural liftings of vector fields to tangent bundles of bundles of $1$ -forms

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 in the view of Cartan geometries

Natural operators lifting functions to affinors on higher order cotangent bundles

Natural operators lifting functions to bundle functors on fibered manifolds

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 lifting vector fields to bundles of Weil contact elements

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 projectors in tensor spaces.

Natural pseudodistances between closed surfaces

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

Currently displaying 21 – 40 of 238