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Dostęp zamkniętyA general method to construct invariant PDEs on homogeneous manifolds
| dc.abstract.en | Let M=G/H be an (n+1)-dimensional homogeneous manifold and Jk(n,M)=:Jk be the manifold of k-jets of hypersurfaces of M. The Lie group G acts naturally on each Jk. 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 E⊂Jk. 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 Sn+1. Our method works under some mild assumptions on the action of G, namely: A1) the group G must have an open orbit in Jk−1, and A2) the stabilizer H(k−1)⊂G of the fiber Jk→Jk−1 must factorize via the group of translations of the fiber itself. |
| dc.affiliation | Uniwersytet Warszawski |
| dc.contributor.author | Moreno, Giovanni |
| dc.contributor.author | Manno, Gianni |
| dc.contributor.author | Gutt, Jan |
| dc.contributor.author | Alekseevsky, Dmitri V. |
| dc.date.accessioned | 2024-01-24T17:37:49Z |
| dc.date.available | 2024-01-24T17:37:49Z |
| dc.date.issued | 2022 |
| dc.description.finance | Publikacja bezkosztowa |
| dc.identifier.doi | 10.1142/S0219199720500893 |
| dc.identifier.issn | 0219-1997 |
| dc.identifier.uri | https://repozytorium.uw.edu.pl//handle/item/101566 |
| dc.identifier.weblink | https://www.worldscientific.com/doi/10.1142/S0219199720500893 |
| dc.language | eng |
| dc.pbn.affiliation | mathemathics |
| dc.relation.ispartof | Communications in Contemporary Mathematics |
| dc.relation.pages | 2050089 |
| dc.rights | ClosedAccess |
| dc.sciencecloud | nosend |
| dc.title | A general method to construct invariant PDEs on homogeneous manifolds |
| dc.type | JournalArticle |
| dspace.entity.type | Publication |