| Autor: |
Constantinescu, Oana |
| Rok vydání: |
2012 |
| Předmět: |
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| Zdroj: |
SIGMA 8 (2012), 059, 17 pages |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.3842/SIGMA.2012.059 |
| Popis: |
We address the integrability conditions of the inverse problem of the calculus of variations for time-dependent SODE using the Spencer version of the Cartan-K\"ahler theorem. We consider a linear partial differential operator $P$ given by the two Helmholtz conditions expressed in terms of semi-basic 1-forms and study its formal integrability. We prove that $P$ is involutive and there is only one obstruction for the formal integrability of this operator. The obstruction is expressed in terms of the curvature tensor $R$ of the induced nonlinear connection. We recover some of the classes of Lagrangian semisprays: flat semisprays, isotropic semisprays and arbitrary semisprays on 2-dimensional manifolds. |
| Databáze: |
arXiv |
| Externí odkaz: |
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