Displaying similar documents to “Natural liftings of foliations to the r -tangent bunde”

Lifts of Foliated Linear Connectionsto the Second Order Transverse Bundles

Vadim V. Shurygin, Svetlana K. Zubkova (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The second order transverse bundle T 2 M of a foliated manifold M carries a natural structure of a smooth manifold over the algebra 𝔻 2 of truncated polynomials of degree two in one variable. Prolongations of foliated mappings to second order transverse bundles are a partial case of more general 𝔻 2 -smooth foliated mappings between second order transverse bundles. We establish necessary and sufficient conditions under which a 𝔻 2 -smooth foliated diffeomorphism between two second order transverse...

The generic dimension of the first derived system

Robert P. Buemi (1978)

Annales de l'institut Fourier

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Any r -dimensional subbundle of the cotangent bundle on an n -dimensional manifold M partitions M into subsets M 0 , ... , M m ( m being the minimum of r and C ( n - r , 2 ) , the combinations of n - r things taken 2 at a time). M i is the set on which the first derived systems of the subbundle has codimension i . In this paper we prove the following: Theorem. Let s ≥ 2 and let Q be a generic C s r -dimensional subbundle of the cotangent bundle of an n -dimensional manifold M . The codimension...

Correspondence between diffeomorphism groups and singular foliations

Tomasz Rybicki (2012)

Annales Polonici Mathematici

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It is well-known that any isotopically connected diffeomorphism group G of a manifold determines a unique singular foliation ℱ G . A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism groups is established. As an illustration of this correspondence it is shown that the commutator subgroup [G,G] of an isotopically connected, factorizable and non-fixing C r diffeomorphism group G is simple iff the foliation ℱ [ G , G ] defined by [G,G] admits no proper...

Warped compact foliations

Szymon M. Walczak (2008)

Annales Polonici Mathematici

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The notion of the Hausdorffized leaf space ˜ of a foliation is introduced. A sufficient condition for warped compact foliations to converge to ˜ is given. Moreover, a necessary condition for warped compact Hausdorff foliations to converge to ˜ is shown. Finally, some examples are examined.

Linear liftings of affinors to Weil bundles

Jacek Dębecki (2003)

Colloquium Mathematicae

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We give a classification of all linear natural operators transforming affinors on each n-dimensional manifold M into affinors on T A M , where T A is the product preserving bundle functor given by a Weil algebra A, under the condition that n ≥ 2.

The natural operators lifting vector fields to generalized higher order tangent bundles

Włodzimierz M. Mikulski (2000)

Archivum Mathematicum

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For natural numbers r and n and a real number a we construct a natural vector bundle T ( r ) , a over n -manifolds such that T ( r ) , 0 is the (classical) vector tangent bundle T ( r ) of order r . For integers r ≥ 1 and n ≥ 3 and a real number a < 0 we classify all natural operators T | M n ⇝ T T ( r ) , a lifting vector fields from n -manifolds to T ( r ) , a .