A general method to construct invariant PDEs on homogeneous manifolds

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F22%3A50019343" target="_blank" >RIV/62690094:18470/22:50019343 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.worldscientific.com/doi/abs/10.1142/S0219199720500893" target="_blank" >https://www.worldscientific.com/doi/abs/10.1142/S0219199720500893</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0219199720500893" target="_blank" >10.1142/S0219199720500893</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A general method to construct invariant PDEs on homogeneous manifolds

Popis výsledku v původním jazyce

Let M = G/H be an (n + 1)-dimensional homogeneous manifold and J(k)(n, M) =: J(k) be the manifold of k-jets of hypersurfaces of M. The Lie group G acts naturally on each J(k). A G-invariant partial differential equation of order k for hypersurfaces of M (i.e., with n independent variables and 1 dependent one) is defined as a G-invariant hypersurface epsilon subset of J(k). We describe a general method for constructing such invariant partial differential equations for k &gt;= 2. The problem reduces to the description of hypersurfaces, in a certain vector space, which are invariant with respect to the linear action of the stability subgroup H(k-1) of the (k - 1)-prolonged action of G. We apply this approach to describe invariant partial differential equations for hypersurfaces in the Euclidean space En+1 and in the conformal space S-n+(1). Our method works under some mild assumptions on the action of G, namely: A1) the group G must have an open orbit in J(k-1), and A2) the stabilizer H(k-1) subset of G of the fiber J(k) -&gt; J(k-1) must factorize via the group of translations of the fiber itself.

Název v anglickém jazyce

A general method to construct invariant PDEs on homogeneous manifolds

Popis výsledku anglicky

Let M = G/H be an (n + 1)-dimensional homogeneous manifold and J(k)(n, M) =: J(k) be the manifold of k-jets of hypersurfaces of M. The Lie group G acts naturally on each J(k). A G-invariant partial differential equation of order k for hypersurfaces of M (i.e., with n independent variables and 1 dependent one) is defined as a G-invariant hypersurface epsilon subset of J(k). We describe a general method for constructing such invariant partial differential equations for k &gt;= 2. The problem reduces to the description of hypersurfaces, in a certain vector space, which are invariant with respect to the linear action of the stability subgroup H(k-1) of the (k - 1)-prolonged action of G. We apply this approach to describe invariant partial differential equations for hypersurfaces in the Euclidean space En+1 and in the conformal space S-n+(1). Our method works under some mild assumptions on the action of G, namely: A1) the group G must have an open orbit in J(k-1), and A2) the stabilizer H(k-1) subset of G of the fiber J(k) -&gt; J(k-1) must factorize via the group of translations of the fiber itself.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-00496S" target="_blank" >GA18-00496S: Singulární prostory ze speciální holonomie a foliací</a><br>

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Communications in Contemporary Mathematics

ISSN

0219-1997

e-ISSN

1793-6683

Svazek periodika

24

Číslo periodika v rámci svazku

03

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

26

Strana od-do

"Article Number: 2050089"

Kód UT WoS článku

000773516800008

EID výsledku v databázi Scopus

2-s2.0-85099164798