Publication result detail

The Legendre-like operators on tuples of Lagrangians and functions

DOUPOVEC, M.; KUREK, J.; MIKULSKI, W.

Original Title

The Legendre-like operators on tuples of Lagrangians and functions

English Title

The Legendre-like operators on tuples of Lagrangians and functions

Type

Scopus Article

Original Abstract

Let Y be a fibred manifold with an m-dimensional basis M. We describe all Legendre-like operators C, i.e. natural operators transforming tuples (λ, g) of Lagrangians λ: JsY →∧m T∗M and functions g: M → R (resp. g: Y → R) into Legendre maps C(λ, g): ∧ JsY → SsT M ⊗ V∗Y ⊗ m T∗M. The most important example of such operators is the Legendre operator (from the variational calculus) being the one in question depending only on Lagrangians.

English abstract

Let Y be a fibred manifold with an m-dimensional basis M. We describe all Legendre-like operators C, i.e. natural operators transforming tuples (λ, g) of Lagrangians λ: JsY →∧m T∗M and functions g: M → R (resp. g: Y → R) into Legendre maps C(λ, g): ∧ JsY → SsT M ⊗ V∗Y ⊗ m T∗M. The most important example of such operators is the Legendre operator (from the variational calculus) being the one in question depending only on Lagrangians.

Keywords

Fibred manifolds | Lagrangians | Legendre maps | Legendre transformation | natural operators

Key words in English

Fibred manifolds | Lagrangians | Legendre maps | Legendre transformation | natural operators

Authors

DOUPOVEC, M.; KUREK, J.; MIKULSKI, W.

Released

01.01.2025

Periodical

Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica

Volume

1

Number

79

State

Republic of Poland

Pages from

1

Pages to

12

Pages count

12

URL

https://journals.umcs.pl/a/article/view/19840

BibTex

@article{BUT199248,
  author="Miroslav {Doupovec} and  {} and  {}",
  title="The Legendre-like operators on tuples of Lagrangians and functions",
  journal="Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica",
  year="2025",
  volume="1",
  number="79",
  pages="1--12",
  doi="10.17951/a.2025.79.1.1-12",
  url="https://journals.umcs.pl/a/article/view/19840"
}