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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2016

Confidentiality

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

Name of the periodical

Differential Geometry and its Application

ISSN

0926-2245

e-ISSN

—

Volume of the periodical

2016

Issue of the periodical within the volume

49

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

21

Pages from-to

351-371

UT code for WoS article

000389092700019

EID of the result in the Scopus database

2-s2.0-84992110685