p-Almost tangent structures

León, Manuel de; Méndez, Isabel García; Salgado, Modesto

doi:10.1007/bf02844526

Cited by 40 publications

(73 citation statements)

References 6 publications

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“…is a sopde, from Proposition 6 we know that, if it is integrable, then its integral sections are first prolongations φ (1) : R k → T 1 k Q of maps φ : R k → Q, and from (29) we deduce that φ is a solution to the Euler-Lagrange equations (22).…”

Section: Lagrangian Formalism: K-symplectic Lagrangian Systemsmentioning

confidence: 93%

SYMMETRIES AND CONSERVATION LAWS IN THE GÜNTHER k-SYMPLECTIC FORMALISM OF FIELD THEORY

Román‐Roy¹,

Salgado

Vilariño

2007

Rev. Math. Phys.

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This paper is devoted to studying symmetries of k-symplectic Hamiltonian and Lagrangian first-order classical field theories. In particular, we define symmetries and Cartan symmetries and study the problem of associating conservation laws to these symmetries, stating and proving Noether's theorem in different situations for the Hamiltonian and Lagrangian cases. We also characterize equivalent Lagrangians, which lead to an introduction of Lagrangian gauge symmetries, as well as analyzing their relation with Cartan symmetries.

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Section: Lagrangian Formalism: K-symplectic Lagrangian Systemsmentioning

confidence: 93%

SYMMETRIES AND CONSERVATION LAWS IN THE GÜNTHER k-SYMPLECTIC FORMALISM OF FIELD THEORY

Román‐Roy¹,

Salgado

Vilariño

2007

Rev. Math. Phys.

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“…To close this introduction we wish to emphasize that our notion of multisymplectic structure should be clearly distinguished from certain other structures which have recently been discussed in the literature such as, for instance, ifc-almost cotangent structures [20]. The latter, in particular, constitute a generalization of the so-called polysymplectic structures [13] and fe-symplectic structures [2,3].…”

Section: Introductionmentioning

confidence: 99%

On the geometry of multisymplectic manifolds

1999

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A multisymplectic structure on a manifold is defined by a closed differential form with zero characteristic distribution. Starting from the linear case, some of the basic properties of multisymplectic structures are described. Various examples of multisymplectic manifolds are considered, and special attention is paid to the canonical multisymplectic structure living on a bundle of exterior fc-forms on a manifold. For a class of multisymplectic manifolds admitting a 'Lagrangian' fibration, a general structure theorem is given which, in particular, leads to a classification of these manifolds in terms of a prescribed family of cohomology classes.1991 Mathematics subject classification (Amer. Math. Soc): primary 53C15, 58Axx.

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“…In this section we briefly recall some well-known facts about tangent bundles of k 1 -velocities (we refer the reader to [13,14,18,19,20] for more details).…”

Section: Geometric Preliminairesmentioning

confidence: 99%