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Multisymplectic forms of degree three in dimension seven

Bureš, Jarolím, Vanžura, Jiří (2003)

Proceedings of the 22nd Winter School "Geometry and Physics"

A multisymplectic 3-structure on an n -dimensional manifold M is given by a closed smooth 3-form ω of maximal rank on M which is of the same algebraic type at each point of M , i.e. they belong to the same orbit under the action of the group G L ( n , ℝ ) . This means that for each point x ∈ M the form ω x is isomorphic to a chosen canonical 3-form on ℝ n . R. Westwick [Linear Multilinear Algebra 10, 183–204 (1981; Zbl 0464.15001)] and D. Ž. Djoković [Linear Multilinear Algebra 13, 3–39 (1983; Zbl 0515.15011)] obtained...

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 ,...

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