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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...On a construction connecting Lie algebras with general algebras Michor, Peter W., Ruppert, W., Wegenkittl, K.

(1989) Proceedings of the Winter School "Geometry and Physics"On boundary value problem of Neumann type for hypercomplex function with values in a Clifford algebra Xu, Zhenyuan

(1990) Proceedings of the Winter School "Geometry and Physics"On cotangent bundles of some natural bundles Kolář, Ivan

(1994) Proceedings of the Winter School "Geometry and Physics" The author studies relations between the following two types of natural operators: 1. Natural operators transforming vector fields on manifolds into vector fields on a natural bundle F; 2. Natural operators transforming vector fields on manifolds into functions on the cotangent bundle of F . It is deduced that under certain assumptions on F, all natural operators of the second type can be constructed through those of the first one.On Finsler-Weyl manifolds and connections Kozma, L.

(1996) Proceedings of the 15th Winter School "Geometry and Physics" Let M be a manifold with all structures smooth which admits a metric g . Let Γ be a linear connection on M such that the associated covariant derivative \nabla satisfies \nabla g = g \otimes w for some 1-form w on M . Then one refers to the above setup as a Weyl structure on M and says that the pair (g, w) fits Γ . If σ : M \to ℝ and if (g, w) fits Γ, then (e^{σ g}, w + d σ) fits Γ . Thus if one thinks of this as a map g \mapsto w, then e^{σ g} \mapsto w + d σ .In this paper, the author attempts to apply Weyl’s idea above to Finsler spaces. A Finsler fundamental function L : T M \to ℝ satisfies (i) L (u) > 0 for...On local flatness of manifolds with AHS-structures Čap, Andreas, Slovák, Jan

(1996) Proceedings of the 15th Winter School "Geometry and Physics" Summary: The AHS-structures on manifolds are the simplest cases of the so called parabolic geometries which are modeled on homogeneous spaces corresponding to a parabolic subgroup in a semisimple Lie group. It covers the cases where the negative parts of the graded Lie algebras in question are abelian. In the series the authors developed a consistent frame bundle approach to the subject. Here we give explicit descriptions of the obstructions against the flatness of such structures based on the latter...On mutational deformation retracts Sanjurjo, José M. R.

(1989) Proceedings of the Winter School "Geometry and Physics"On peculiarity of the p = 2 case among the p -state Ising-like models. Kwaśniewski, A. K.

(1989) Proceedings of the Winter School "Geometry and Physics"On sectioning tangent bundles and other vector bundles Korbaš, Július, Zvengrowski, Peter

(1996) Proceedings of the Winter School "Geometry and Physics" This paper has two parts. Part one is mainly intended as a general introduction to the problem of sectioning vector bundles (in particular tangent bundles of smooth manifolds) by everywhere linearly independent sections, giving a survey of some ideas, methods and results.Part two then records some recent progress in sectioning tangent bundles of several families of specific manifolds.On some rational fibrations with nonvanishing Massey products over homogeneous spaces Tralle, Alexei

(1994) Proceedings of the Winter School "Geometry and Physics" The main result of this brief note asserts, incorrectly, that there exists a rational fibration S^{2} \to E \to ℂ P^{3} whose total space admits nonzero Massey products. The methods used would be appropriate for showing results of this kind, if the circumstances were to allow for it. Unfortunately the author makes a simple, but nonetheless fatal, computational error in his calculation that ostensibly shows the existence of a nonzero Massey product (p. 249, 1.13: a b \neq D (x^{2} y)) . In fact, for any rational fibration S^{2} \to E \to ℂ P^{3} the total space...On sprays and connections Kozma, László

(1990) Proceedings of the Winter School "Geometry and Physics" [For the entire collection see Zbl 0699.00032.] A connection structure (M,H) and a path structure (M,S) on the manifold M are called compatible, if S (v) = H (v, v), \forall v \in T M, locally G^{i} (x, y) = y^{j} Γ_{j}^{i} (x, y), where G^{i} and Γ_{j}^{i} express the semi-spray S and the connection map H, resp. In the linear case of H its geodesic spray S is quadratic: G^{i} (x, y) = Γ_{j k}^{i} (k) y^{j} y^{k} . On the contrary, the homogeneity condition of S induces the relation for the compatible connection H, y^{j} (Γ_{j}^{i} \circ μ_{t}) = t y^{j} Γ_{j}^{i}, whence it follows not that H is linear, i.e. if a connection structure is compatible with a spray, then...Currently displaying 61 -
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Displaying 61 – 80 of 125

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

On a construction connecting Lie algebras with general algebras

On boundary value problem of Neumann type for hypercomplex function with values in a Clifford algebra

On cotangent bundles of some natural bundles

On Finsler-Weyl manifolds and connections

On local flatness of manifolds with AHS-structures

On mutational deformation retracts

On peculiarity of the $p = 2$ case among the $p$ -state Ising-like models.

On sectioning tangent bundles and other vector bundles

On some rational fibrations with nonvanishing Massey products over homogeneous spaces

On sprays and connections

Currently displaying 61 – 80 of 125