All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 4 Next

Displaying 61 – 80 of 205

Showing per page

Forms equivalent to curvatures.

Horacio Porta, Lázaro Recht (1986)

Revista Matemática Iberoamericana

The 2-forms, Ω and Ω' on a manifold M with values in vector bundles ξ --> M and ξ' --> M are equivalent if there exist smooth fibered-linear mapsξ --> ξ' and W: ξ --> ξ' with Ω' = UΩ and Ω = WΩ'. It is shown that an ordinary 2-form equivalent to the curvature of a linear connection has locally a non-vanishing integrating factor at each point in the interior of the set rank (ω) = 2 or in the set rank (ω) > 2. Under favorable conditions the same holds at points where...

Geometry and representation of the singular symplectic forms

Wojciech Domitrz, Stanisław Janeczko, Zbigniew Pasternak-Winiarski (2003)

Banach Center Publications

In this paper we show to what extent the closed, singular 2-forms are represented, up to the smooth equivalence, by their restrictions to the corresponding singularity set. In the normalization procedure of the singularity set we find the sufficient conditions for the given closed 2-form to be a pullback of the classical Darboux form. We also find the classification list of simple singularities of the maximal isotropic submanifold-germs in the codimension one Martinet's singular symplectic structures....

Growth of a primitive of a differential form

Jean-Claude Sikorav (2001)

Bulletin de la Société Mathématique de France

For an exact differential form on a Riemannian manifold to have a primitive bounded by a given function f , by Stokes it has to satisfy some weighted isoperimetric inequality. We show the converse up to some constants if M has bounded geometry. For a volume form, it suffices to have the inequality ( | Ω | ≤ ∫ ∂ Ω f d σ for every compact domain Ω ⊂ M ). This implies in particular the “well-known” result that if M is the universal covering of a compact Riemannian manifold with non-amenable fundamental group, then the volume...

Homogeneous variational problems: a minicourse

David J. Saunders (2011)

Communications in Mathematics

A Finsler geometry may be understood as a homogeneous variational problem, where the Finsler function is the Lagrangian. The extremals in Finsler geometry are curves, but in more general variational problems we might consider extremal submanifolds of dimension m . In this minicourse we discuss these problems from a geometric point of view.

Induced differential forms on manifolds of functions

Cornelia Vizman (2011)

Archivum Mathematicum

Differential forms on the Fréchet manifold ℱ ( S , M ) of smooth functions on a compact k -dimensional manifold S can be obtained in a natural way from pairs of differential forms on M and S by the hat pairing. Special cases are the transgression map Ω p ( M ) → Ω p - k ( ℱ ( S , M ) ) (hat pairing with a constant function) and the bar map Ω p ( M ) → Ω p ( ℱ ( S , M ) ) (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians [6].

Intégrales premières d'une forme de Pfaff analytique

Jean-François Mattei, Robert Moussu (1978)

Annales de l'institut Fourier

Soit ω un germe en 0 ∈ C n de 1-forme différentielle holomorphe vérifiant la condition d’intégrabilité ω ∧ d ω = 0 . S’il existe un germe h d’application holomorphe de ( C r , 0 ) dans ( C n , 0 ) qui possède les deux propriétés suivantes :a) h * ( ω ) a une intégrale première formelle,b) la codimension du lieu singulier S ( h * ( ω ) ) de h * ( ω ) est supérieure ou égale à 2,alors ω a une intégrale première holomorphe.

Currently displaying 61 – 80 of 205