A general method to construct invariant PDEs on homogeneous manifolds

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>

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 >= 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) -> J(k-1) must factorize via the group of translations of the fiber itself.
Czech name
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Czech description
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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

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)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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