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Global generalized Bianchi identities for invariant variational problems on gauge-natural bundles

Marcella Palese, Ekkehart Winterroth (2005)

Archivum Mathematicum

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...

Hidden symmetries of the gravitational contact structure of the classical phase space of general relativistic test particle

Josef Janyška (2014)

Archivum Mathematicum

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 Cartan connections

Juraj Virsik (1996)

Archivum Mathematicum

A Cartan connection associated with a pair P ( M , G ' ) ⊂ P ( M , G ) is defined in the usual manner except that only the injectivity of ω : T ( P ' ) → T ( G ) e is required. For an r -th order connection associated with a bundle morphism Φ : P ' → P the concept of Cartan order q ≤ r is defined, which for q = r = 1 , Φ : P ' ⊂ P , and dim M = dim G / G ' coincides with the classical definition. Results are obtained concerning the Cartan order of r -th order connections that are the product of r first order (Cartan) connections.

Higher order connections.

Eastwood, Michael G. (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Higher order jet involution

Miroslav Doupovec, Włodzimierz M. Mikulski (2007)

Czechoslovak Mathematical Journal

We introduce an exchange natural isomorphism between iterated higher order jet functors depending on a classical linear connection on the base manifold. As an application we study the prolongation of higher order connections to jet bundles.

Higher order linear connections from first order ones

Włodzimierz M. Mikulski (2007)

Archivum Mathematicum

We describe how find all ℳ f m -natural operators D transforming torsion free classical linear connections ∇ on m -manifolds M into r -th order linear connections D ( ∇ ) on M .

Higher order valued reduction theorems for classical connections

Josef Janyška (2005)

Open Mathematics

We generalize reduction theorems for classical connections to operators with values in k-th order natural bundles. Using the 2nd order valued reduction theorems we classify all (0,2)-tensor fields on the cotangent bundle of a manifold with a linear (non-symmetric) connection.

Holomorphic extension maps for spaces of Whitney jets.

Jean Schmets, Manuel Valdivia (2001)

RACSAM

The key result (Theorem 1) provides the existence of a holomorphic approximation map for some space of C∞-functions on an open subset of Rn. This leads to results about the existence of a continuous linear extension map from the space of the Whitney jets on a closed subset F of Rn into a space of holomorphic functions on an open subset D of Cn such that D ∩ Rn = RnF.

Currently displaying 81 – 100 of 390