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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 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 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...Nielsen theory and related topics. Proceedings of the international conference, St. John's, Newfoundland, Canada, June 28-July 2, 2004. Heath, Philip R. (ed.), Brown, Robert F. (ed.), Keppelmann, Edward C. (ed.)

(2006) Fixed Point Theory and Applications [electronic only]Note on Stieffel-Whitney classes of flag manifolds Korbaš, Július

(1987) Proceedings of the Winter School "Geometry and Physics"Notes on conformal differential geometry Eastwood, Michael

(1996) Proceedings of the 15th Winter School "Geometry and Physics" This survey paper presents lecture notes from a series of four lectures addressed to a wide audience and it offers an introduction to several topics in conformal differential geometry. In particular, a very nice and gentle introduction to the conformal Riemannian structures themselves, flat or curved, is presented in the beginning. Then the behavior of the covariant derivatives under the rescaling of the metrics is described. This leads to Penrose’s local twistor transport which is introduced in...Currently displaying 1 -
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Natural liftings of foliations to the $r$ -tangent bunde

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 Lagrangians

Natural transformations of Weil functors into bundle functors

Nielsen theory and related topics. Proceedings of the international conference, St. John's, Newfoundland, Canada, June 28–July 2, 2004.

Note on Stieffel-Whitney classes of flag manifolds

Notes on conformal differential geometry

Currently displaying 1 – 10 of 10