The Legendre maps from two Lagrangians or from a Lagrangian and a p-form
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F26%3A0199250" target="_blank" >RIV/00216305:26210/26:0199250 - isvavai.cz</a>
Result on the web
<a href="https://journals.umcs.pl/a/article/view/19841/12578" target="_blank" >https://journals.umcs.pl/a/article/view/19841/12578</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.17951/a.2025.79.1.13-23" target="_blank" >10.17951/a.2025.79.1.13-23</a>
Alternative languages
Result language
angličtina
Original language name
The Legendre maps from two Lagrangians or from a Lagrangian and a p-form
Original language description
Let FMm,n denote the category of fibered manifolds with mdimensional bases and n-dimensional fibres and their fibered local diffeomorphisms. We prove that if m, n and s are positive integers, then any FMm,n-natural operator C transforming tuples (λ1, λ2) of Lagrangians λ1, λ2: JsY → ∧m T∗M on FMm,n-objects Y → M into Legendre maps C(λ1, λ2): JsY → SsT M ⊗ V∗Y ⊗∧m T∗M on Y is of the form C(λ1, λ2) = c1Λ(λ1) + c2Λ(λ2), c1, c2 ∈ R, where Λ is the Legendre operator. We also prove that if m, n, s and p are positive integers, then any FMm,n-natural operator C transforming tuples (λ, η) of Lagrangians λ: JsY →∧m T∗M and p-forms η ∈ Ωp(M) into Legendre maps C(λ, η): JsY → SsT M ⊗ V∗Y ⊗∧m T∗M is of the form C(λ, η) = cΛ(λ), c ∈ R, where Λ is the Legendre operator.
Czech name
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Czech description
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Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10100 - Mathematics
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica
ISSN
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e-ISSN
2083-7402
Volume of the periodical
1
Issue of the periodical within the volume
79
Country of publishing house
PL - POLAND
Number of pages
11
Pages from-to
13-23
UT code for WoS article
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EID of the result in the Scopus database
2-s2.0-105012868343