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A general method to construct invariant PDEs on homogeneous manifolds

The result's identifiers

  • Result code in 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>

  • Result on the web

    <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>

Alternative languages

  • Result language

    angličtina

  • Original language name

    A general method to construct invariant PDEs on homogeneous manifolds

  • Original language description

    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.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

    <a href="/en/project/GA18-00496S" target="_blank" >GA18-00496S: Singular spaces from special holonomy and foliations</a><br>

  • Continuities

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

Others

  • Publication year

    2022

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Communications in Contemporary Mathematics

  • ISSN

    0219-1997

  • e-ISSN

    1793-6683

  • Volume of the periodical

    24

  • Issue of the periodical within the volume

    03

  • Country of publishing house

    SG - SINGAPORE

  • Number of pages

    26

  • Pages from-to

    "Article Number: 2050089"

  • UT code for WoS article

    000773516800008

  • EID of the result in the Scopus database

    2-s2.0-85099164798