-invariant variational principles on frame bundles.
Glättung endlich-differenzierbarer Räume.
Global generalized Bianchi identities for invariant variational problems on gauge-natural bundles
We derive both local and global generalized Bianchi identities for classical Lagrangian field theories on gauge-natural bundles. We show that globally defined generalized Bianchi identities can be found without the a priori introduction of a connection. The proof is based on a global decomposition of the variational Lie derivative of the generalized Euler-Lagrange morphism and the representation of the corresponding generalized Jacobi morphism on gauge-natural bundles. In particular, we show that...
Gluing of differentiable spaces and applications.
Graded Poisson structures on the algebra of differential forms.
Gradient horizontal de fonctions polynomiales
Nous étudions les trajectoires du gradient sous-riemannien (appellé horizontal) de fonctions polynômes. Dans ce cadre l’inégalité de Łojasiewicz n’est pas valide et une trajectoire du gradient horizontal peut être de longueur infinie, et peut même s’accumuler sur une courbe fermée. Nous montrons que ces comportement sont exceptionnels ; et que, pour une fonction générique les trajectoires de son gradient horizontal ont des propriétés similaires au cas du gradient riemannien. Pour obtenir la finitude...
Groupes d’automorphismes de et équations différentielles
Groups of Isometric Transformations, Basic Connections and Splitting results on Riemannian Manifolds
Growth of a primitive of a differential form
For an exact differential form on a Riemannian manifold to have a primitive bounded by a given function , by Stokes it has to satisfy some weighted isoperimetric inequality. We show the converse up to some constants if has bounded geometry. For a volume form, it suffices to have the inequality ( for every compact domain ). This implies in particular the “well-known” result that if is the universal covering of a compact Riemannian manifold with non-amenable fundamental group, then the volume...
Harmonic cohomology classes of symplectic manifolds.
Harmonic mappings of Kähler manifolds to locally symmetric spaces
Harmonie Forms Dual to Geodesic Cycles in Quotients of SU (p, 1).
Hecke operators on de Rham cohomology.
We introduce Hecke operators on de Rham cohomology of compact oriented manifolds. When the manifold is a quotient of a Hermitian symmetric domain, we prove that certain types of such operators are compatible with the usual Hecke operators on automorphic forms.
Helmholtz conditions and their generalizations.
Hermitian natural tensors.
Hidden symmetries of the gravitational contact structure of the classical phase space of general relativistic test particle
The phase space of general relativistic test particle is defined as the 1-jet space of motions. A Lorentzian metric defines the canonical contact structure on the odd-dimensional phase space. In the paper we study infinitesimal symmetries of the gravitational contact phase structure which are not generated by spacetime infinitesimal symmetries, i.e. they are hidden symmetries. We prove that Killing multivector fields admit hidden symmetries of the gravitational contact phase structure and we give...
Higher order absolute differentiation with respect to generalized connections
Higher order Cartan connections.
Higher order Cartan connections
A Cartan connection associated with a pair is defined in the usual manner except that only the injectivity of is required. For an -th order connection associated with a bundle morphism the concept of Cartan order is defined, which for , and coincides with the classical definition. Results are obtained concerning the Cartan order of -th order connections that are the product of first order (Cartan) connections.
Higher order connections.