The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Geometric structures on spaces of weighted submanifolds.”

On implicit Lagrangian differential systems

S. Janeczko (2000)

Annales Polonici Mathematici

Similarity:

Let (P,ω) be a symplectic manifold. We find an integrability condition for an implicit differential system D' which is formed by a Lagrangian submanifold in the canonical symplectic tangent bundle (TP,ὡ).

Induced differential forms on manifolds of functions

Cornelia Vizman (2011)

Archivum Mathematicum

Similarity:

Differential forms on the Fréchet manifold ( 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 ( ( S , M ) ) (hat pairing with a constant function) and the bar map Ω p ( M ) Ω p ( ( S , M ) ) (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians [6].

Canonical symplectic structures on the r-th order tangent bundle of a symplectic manifold.

Jan Kurek, Wlodzimierz M. Mikulski (2006)

Extracta Mathematicae

Similarity:

We describe all canonical 2-forms Λ(ω) on the r-th order tangent bundle TM = J (;M) of a symplectic manifold (M, ω). As a corollary we deduce that all canonical symplectic structures Λ(ω) on TM over a symplectic manifold (M, ω) are of the form Λ(ω) = Σ αω for all real numbers α with α ≠ 0, where ω is the (k)-lift (in the sense of A. Morimoto) of ω to TM.

Systems of rays in the presence of distribution of hyperplanes

S. Janeczko (1995)

Banach Center Publications

Similarity:

Horizontal systems of rays arise in the study of integral curves of Hamiltonian systems v H on T*X, which are tangent to a given distribution V of hyperplanes on X. We investigate the local properties of systems of rays for general pairs (H,V) as well as for Hamiltonians H such that the corresponding Hamiltonian vector fields v H are horizontal with respect to V. As an example we explicitly calculate the space of horizontal geodesics and the corresponding systems of rays for the canonical...