Jets and contact elements

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F00%3A00000048" target="_blank" >RIV/47813059:19610/00:00000048 - isvavai.cz</a>

Výsledek na webu

—

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

Jets and contact elements

Popis výsledku v původním jazyce

The purpose of this research-expository work is to introduce basic concepts of the theory of jets, and to study their general properties. An r-jet of a real function of several real variables at a point is simply the collection of the coefficients of ther-th Taylor polynomial of f at this point. The concept of an r-jet is easily generalized to differentiable mappings of smooth manifolds in terms of charts. The structure of the following manifolds of jets is discussed: (a) higher order differential groups, (b) jets of mappings of a Euclidean space into a manifold, with source at the origin (velocities, regular velocities, higher order frames), (c) manifolds of contact elements (higher order Grassmann prolongations of a manifold), i.e., the quotients ofmanifolds of regular velocities by the differential groups acting on them. (d) jet prolongations of fibered manifolds and fibrations, (e) jet prolongations of Lie groups, Lie group actions, principal and associated bundles.

Název v anglickém jazyce

Jets and contact elements

Popis výsledku anglicky

The purpose of this research-expository work is to introduce basic concepts of the theory of jets, and to study their general properties. An r-jet of a real function of several real variables at a point is simply the collection of the coefficients of ther-th Taylor polynomial of f at this point. The concept of an r-jet is easily generalized to differentiable mappings of smooth manifolds in terms of charts. The structure of the following manifolds of jets is discussed: (a) higher order differential groups, (b) jets of mappings of a Euclidean space into a manifold, with source at the origin (velocities, regular velocities, higher order frames), (c) manifolds of contact elements (higher order Grassmann prolongations of a manifold), i.e., the quotients ofmanifolds of regular velocities by the differential groups acting on them. (d) jet prolongations of fibered manifolds and fibrations, (e) jet prolongations of Lie groups, Lie group actions, principal and associated bundles.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2000

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings of the Seminar on Differential Geometry

ISBN

ISBN80-7248-104

ISSN

—

e-ISSN

—

Počet stran výsledku

48

Strana od-do

—

Název nakladatele

Slezská Univerzita v Opavě, Opava

Místo vydání

Opava, ČR

Místo konání akce

—

Datum konání akce

—

Typ akce podle státní příslušnosti

—

Kód UT WoS článku

—