On the geometry of Grassmannian equivalent connections
| dc.creator | Manno, Gianni | |
| dc.date | 2006-04-18 | |
| dc.date.accessioned | 2026-07-07T07:11:01Z | |
| dc.date.available | 2026-07-07T07:11:01Z | |
| dc.description | We introduce the equation of n-dimensional totally geodesic submanifolds of a manifold E as a submanifold of the second order jet space of n-dimensional submanifolds of E. Next we study the geometry of n-Grassmannian equivalent connections, that is linear connections without torsion admitting the same equation of n-dimensional totally geodesic submanifolds. We define the n-Grassmannian structure as the equivalence class of such connections, recovering for n=1 the case of theory of projectively equivalent connections. By introducing the equation of parametrized n-dimensional totally geodesic submanifolds as a submanifold of the second order jet space of the trivial bundle on the space of parameters, we discover a relation of covering between the `parametrized' equation and the `unparametrized' one. After having studied symmetries of these equations, we discuss the case in which the space of parameters is equal to R^n. | |
| dc.description | 20 Pages | |
| dc.identifier | https://arxiv.org/abs/math/0604390 | |
| dc.identifier | http://arxiv.org/abs/math/0604390 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111606 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 58A20 (primary), 14M15, 53B10, 70S10 | |
| dc.title | On the geometry of Grassmannian equivalent connections | |
| dc.type | text |