Displaying 21 – 40 of 101

Showing per page

The generic dimension of the first derived system

Robert P. Buemi (1978)

Annales de l'institut Fourier

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...

The geometric complex for algebraic curves with cone-like singularities and admissible Morse functions

Ursula Ludwig (2010)

Annales de l’institut Fourier

In a previous note the author gave a generalisation of Witten’s proof of the Morse inequalities to the model of a complex singular curve X and a stratified Morse function f . In this note a geometric interpretation of the complex of eigenforms of the Witten Laplacian corresponding to small eigenvalues is provided in terms of an appropriate subcomplex of the complex of unstable cells of critical points of f .

The geometry of a closed form

Marisa Fernández, Raúl Ibáñez, Manuel de León (1998)

Banach Center Publications

It is proved that a closed r-form ω on a manifold M defines a cohomology (called ω-coeffective) on M. A general algebraic machinery is developed to extract some topological information contained in the ω-coeffective cohomology. The cases of 1-forms, symplectic forms, fundamental 2-forms on almost contact manifolds, fundamental 3-forms on G 2 -manifolds and fundamental 4-forms in quaternionic manifolds are discussed.

The geometry of the space of Cauchy data of nonlinear PDEs

Giovanni Moreno (2013)

Open Mathematics

First-order jet bundles can be put at the foundations of the modern geometric approach to nonlinear PDEs, since higher-order jet bundles can be seen as constrained iterated jet bundles. The definition of first-order jet bundles can be given in many equivalent ways - for instance, by means of Grassmann bundles. In this paper we generalize it by means of flag bundles, and develop the corresponding theory for higher-oder and infinite-order jet bundles. We show that this is a natural geometric framework...

The graded differential geometry of mixed symmetry tensors

Andrew James Bruce, Eduardo Ibarguengoytia (2019)

Archivum Mathematicum

We show how the theory of 2 n -manifolds - which are a non-trivial generalisation of supermanifolds - may be useful in a geometrical approach to mixed symmetry tensors such as the dual graviton. The geometric aspects of such tensor fields on both flat and curved space-times are discussed.

The inverse problem in the calculus of variations: new developments

Thoan Do, Geoff Prince (2021)

Communications in Mathematics

We deal with the problem of determining the existence and uniqueness of Lagrangians for systems of n second order ordinary differential equations. A number of recent theorems are presented, using exterior differential systems theory (EDS). In particular, we indicate how to generalise Jesse Douglas’s famous solution for n = 2 . We then examine a new class of solutions in arbitrary dimension n and give some non-trivial examples in dimension 3.

The jet prolongations of 2 -fibred manifolds and the flow operator

Włodzimierz M. Mikulski (2008)

Archivum Mathematicum

Let r , s , m , n , q be natural numbers such that s r . We prove that any 2 - 𝕄 m , n , q -natural operator A : T 2-proj T J ( s , r ) transforming 2 -projectable vector fields V on ( m , n , q ) -dimensional 2 -fibred manifolds Y X M into vector fields A ( V ) on the ( s , r ) -jet prolongation bundle J ( s , r ) Y is a constant multiple of the flow operator 𝒥 ( s , r ) .

The natural affinors on ( J r T * ) *

Włodzimierz M. Mikulski (2000)

Archivum Mathematicum

For natural numbers r and n 2 a complete classification of natural affinors on the natural bundle ( J r T * ) * dual to r -jet prolongation J r T * of the cotangent bundle over n -manifolds is given.

The natural affinors on some fiber product preserving gauge bundle functors of vector bundles

Jan Kurek, Włodzimierz M. Mikulski (2006)

Archivum Mathematicum

We classify all natural affinors on vertical fiber product preserving gauge bundle functors F on vector bundles. We explain this result for some more known such F . We present some applications. We remark a similar classification of all natural affinors on the gauge bundle functor F * dual to F as above. We study also a similar problem for some (not all) not vertical fiber product preserving gauge bundle functors on vector bundles.

The natural linear operators T * T T ( r )

J. Kurek, W. M. Mikulski (2003)

Colloquium Mathematicae

For natural numbers n ≥ 3 and r a complete description of all natural bilinear operators T * × f T ( 0 , 0 ) T ( 0 , 0 ) T ( r ) is presented. Next for natural numbers r and n ≥ 3 a full classification of all natural linear operators T * | f T T ( r ) is obtained.

Currently displaying 21 – 40 of 101