dc.contributor.author |
Aminova A. |
|
dc.contributor.author |
Aminov N. |
|
dc.date.accessioned |
2018-09-18T20:16:23Z |
|
dc.date.available |
2018-09-18T20:16:23Z |
|
dc.date.issued |
2006 |
|
dc.identifier.issn |
1064-5616 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/138177 |
|
dc.description.abstract |
It is proved that every projective connection on an n-dimensional manifold M is locally defined by a system script capital L sign of n - 1 second-order ordinary differential equations resolved with respect to the second derivatives and with right-hand sides cubic in the first derivatives, and that every differential system script capital L sign defines a projective connection on M. The notion of equivalent differential systems is introduced and necessary and sufficient conditions are found for a system y to be reducible by a change of variables to a system whose integral curves are straight lines. It is proved that the symmetry group of a differential system script capital L sign is a group of projective transformations in n-dimensional space with the associated projective connection and has dimension ≤ n 2 + 2n. Necessary and sufficient conditions are found for a system to admit the maximal symmetry group; basis vector fields and structure equations of the maximal symmetry Lie algebra are produced. As an application a classification is given of the systems script capital L sign of two second-order differential equations admitting three-dimensional soluble symmetry groups. © 2006 RAS(DoM) and LMS. |
|
dc.relation.ispartofseries |
Sbornik Mathematics |
|
dc.title |
Projective geometry of systems of second-order differential equations |
|
dc.type |
Article |
|
dc.relation.ispartofseries-issue |
7-8 |
|
dc.relation.ispartofseries-volume |
197 |
|
dc.collection |
Публикации сотрудников КФУ |
|
dc.relation.startpage |
951 |
|
dc.source.id |
SCOPUS10645616-2006-197-78-SID33751022006 |
|