Graded jet geometry

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F24%3A00375583" target="_blank" >RIV/68407700:21340/24:00375583 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.geomphys.2024.105250" target="_blank" >https://doi.org/10.1016/j.geomphys.2024.105250</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.geomphys.2024.105250" target="_blank" >10.1016/j.geomphys.2024.105250</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Graded jet geometry

Popis výsledku v původním jazyce

Jet manifolds and vector bundles allow one to employ tools of differential geometry to study differential equations, for example those arising as equations of motions in physics. They are necessary for a geometrical formulation of Lagrangian mechanics and the calculus of variations. It is thus only natural to require their generalization in geometry of Z-graded manifolds and vector bundles. Our aim is to construct the k-th order jet bundle J^k_E of an arbitrary Z-graded vector bundle E over an arbitrary Z-graded manifold M. We do so by directly constructing its sheaf of sections, which allows one to quickly prove all its usual properties. It turns out that it is convenient to start with the construction of the graded vector bundle of k-th order (linear) differential operators D^k_E on E. In the process, we discuss (principal) symbol maps and a subclass of differential operators whose symbols correspond to completely symmetric k-vector fields, thus finding a graded version of Atiyah Lie algebroid. Necessary rudiments of geometry of Z-graded vector bundles over Z-graded manifolds are recalled.

Název v anglickém jazyce

Graded jet geometry

Popis výsledku anglicky

Jet manifolds and vector bundles allow one to employ tools of differential geometry to study differential equations, for example those arising as equations of motions in physics. They are necessary for a geometrical formulation of Lagrangian mechanics and the calculus of variations. It is thus only natural to require their generalization in geometry of Z-graded manifolds and vector bundles. Our aim is to construct the k-th order jet bundle J^k_E of an arbitrary Z-graded vector bundle E over an arbitrary Z-graded manifold M. We do so by directly constructing its sheaf of sections, which allows one to quickly prove all its usual properties. It turns out that it is convenient to start with the construction of the graded vector bundle of k-th order (linear) differential operators D^k_E on E. In the process, we discuss (principal) symbol maps and a subclass of differential operators whose symbols correspond to completely symmetric k-vector fields, thus finding a graded version of Atiyah Lie algebroid. Necessary rudiments of geometry of Z-graded vector bundles over Z-graded manifolds are recalled.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF24-10031K" target="_blank" >GF24-10031K: Gradovaná diferenciální geometrie a její aplikace</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Geometry and Physics

ISSN

0393-0440

e-ISSN

1879-1662

Svazek periodika

203

Číslo periodika v rámci svazku

September

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

31

Strana od-do

—

Kód UT WoS článku

001258966100001

EID výsledku v databázi Scopus

2-s2.0-85196032932