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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 lifts of classical linear connections to the cotangent bundle Kureš, Miroslav

(1996)

Proceedings of the 15th Winter School "Geometry and Physics"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 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 foliations into foliations on the cotangent bundle Mikulski, Włodzimierz M.

(1993) Proceedings of the Winter School "Geometry and Topology"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...n-Cohomology of simple highest weight modules on walls and purity. W. Soergel

(1989) Inventiones mathematicaeNearly regular cell-decompositions of orientable 2-manifolds with at most two exceptional cells Mirko Horňák, Ernest Jucovič

(1977) Mathematica SlovacaNear-rings of continuous functions on compact abelian groups. W. Mutter

(1993) Semigroup forumNecessary Conditions for the Existence of Branched Coverings. Neal Brand

(1979) Inventiones mathematicaeNegatively curved groups and the convergence property. II: Transitivity in negatively curved groups. Freden, Eric M.

(1996) Annales Academiae Scientiarum Fennicae. Series A I. MathematicaNegatively curved groups have the convergence property. I. Freden, Eric M.

(1995) Annales Academiae Scientiarum Fennicae. Series A I. MathematicaNeighborhoods of compacta in euclidean space Gerard Venema

(1980) Fundamenta MathematicaeNeighborly Maps with Few Vertices. T. L. Snyder

(1992) Discrete & computational geometryNeuwirth manifolds and colourings of graphs. Alberto Cavicchioli

(1992) Aequationes mathematicaeNew applications of Luttinger's surgery. Y. Eliashberg, L. Polterovich

(1994) Commentarii mathematici HelveticiNew categorifications of the chromatic and dichromatic polynomials for graphs Marko Stošić

(2006) Fundamenta Mathematicae For each graph G, we define a chain complex of graded modules over the ring of polynomials whose graded Euler characteristic is equal to the chromatic polynomial of G. Furthermore, we define a chain complex of doubly-graded modules whose (doubly) graded Euler characteristic is equal to the dichromatic polynomial of G. Both constructions use Koszul complexes, and are similar to the new Khovanov-Rozansky categorifications of the HOMFLYPT polynomial. We also give a simplified definition of this triply-graded...Currently displaying 1 -
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Natural liftings of foliations to the $r$ -tangent bunde

Natural liftings of foliations to the tangent bundle

Natural lifts of classical linear connections to the cotangent bundle

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 symplectic structures on the tangent bundle of a space-time

Natural transformations of foliations into foliations on the cotangent bundle

Natural transformations of Lagrangians

Natural transformations of Weil functors into bundle functors

n-Cohomology of simple highest weight modules on walls and purity.

Nearly regular cell-decompositions of orientable 2-manifolds with at most two exceptional cells

Near-rings of continuous functions on compact abelian groups.

Necessary Conditions for the Existence of Branched Coverings.

Negatively curved groups and the convergence property. II: Transitivity in negatively curved groups.

Negatively curved groups have the convergence property. I.

Neighborhoods of compacta in euclidean space

Neighborly Maps with Few Vertices.

Neuwirth manifolds and colourings of graphs.

New applications of Luttinger's surgery.

New categorifications of the chromatic and dichromatic polynomials for graphs

Currently displaying 1 – 20 of 111