k-Dirac operator and the Cartan-Kähler theorem for weighted differential operators

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10333480" target="_blank" >RIV/00216208:11320/16:10333480 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.difgeo.2016.09.004" target="_blank" >http://dx.doi.org/10.1016/j.difgeo.2016.09.004</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.difgeo.2016.09.004" target="_blank" >10.1016/j.difgeo.2016.09.004</a>

Jazyk výsledku

angličtina

Název v původním jazyce

k-Dirac operator and the Cartan-Kähler theorem for weighted differential operators

Popis výsledku v původním jazyce

The k-Dirac operator is a first order differential operator which is natural to a particular class of parabolic geometries which include the Lie contact structures. A natural task is to understand the set of local null solutions of the operator at a given point. We will show that this set has a very nice and simple structure, namely we will show that there is a submanifold passing through the point such that any section defined on the submanifold extends locally to a unique null solution of the operator. This result also indicates that these parabolic geometries are naturally associated to a certain constant coefficient operator which has been studied in Clifford analysis and this is the original motivation for this paper. In order to prove the claim about the set of initial conditions for the k-Dirac operator we will adapt some parts of the theory of exterior differential systems and the Cartan-Kähler theorem to the setting of differential operators which are natural to geometric structures that are equipped with a filtration of the tangent bundle.

Název v anglickém jazyce

k-Dirac operator and the Cartan-Kähler theorem for weighted differential operators

Popis výsledku anglicky

The k-Dirac operator is a first order differential operator which is natural to a particular class of parabolic geometries which include the Lie contact structures. A natural task is to understand the set of local null solutions of the operator at a given point. We will show that this set has a very nice and simple structure, namely we will show that there is a submanifold passing through the point such that any section defined on the submanifold extends locally to a unique null solution of the operator. This result also indicates that these parabolic geometries are naturally associated to a certain constant coefficient operator which has been studied in Clifford analysis and this is the original motivation for this paper. In order to prove the claim about the set of initial conditions for the k-Dirac operator we will adapt some parts of the theory of exterior differential systems and the Cartan-Kähler theorem to the setting of differential operators which are natural to geometric structures that are equipped with a filtration of the tangent bundle.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Differential Geometry and its Application

ISSN

0926-2245

e-ISSN

—

Svazek periodika

2016

Číslo periodika v rámci svazku

49

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

21

Strana od-do

351-371

Kód UT WoS článku

000389092700019

EID výsledku v databázi Scopus

2-s2.0-84992110685