Maximal degree variational principles
| dc.creator | Gaeta, G. | |
| dc.creator | Morando, P. | |
| dc.date | 2003-05-14 | |
| dc.date | 2003-12-23 | |
| dc.date.accessioned | 2026-07-07T04:30:11Z | |
| dc.date.available | 2026-07-07T04:30:11Z | |
| dc.description | Let $M$ be smooth $n$-dimensional manifold, fibered over a $k$-dimensional submanifold $B$ as $π:M \to B$, and $\vartheta \in Λ^k (M)$; one can consider the functional on sections $ϕ$ of the bundle $π$ defined by $\int_D ϕ^* (\vartheta)$, with $D$ a domain in $B$. We show that for $k = n-2$ the variational principle based on this functional identifies a unique (up to multiplication by a smooth function) nontrivial vector field in $M$, i.e. a system of ODEs. Conversely, any vector field $X$ on $M$ satisfying $i_X ({\rm d} \vartheta) = 0$ for some $\vartheta \in Λ^{n-2} (M)$ admits such a variational characterization. We consider the general case, and also the particular case $M = P \times R$ where one of the variables (the time) has a distinguished role; in this case our results imply that any Liouville (volume-preserving) vector field on the phase space $P$ admits a variational principle of the kind considered here. | |
| dc.description | Some misprints corrected | |
| dc.identifier | https://arxiv.org/abs/math-ph/0305030 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0305030 | |
| dc.identifier | Diff. Geom. Appl. 21 (2004), 27-40 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57390 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Differential Geometry | |
| dc.subject | 58A15; 34A26; 37C10; 70G75 | |
| dc.title | Maximal degree variational principles | |
| dc.type | text |