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001-es BibID:	BIBFORM019363
Első szerző:	Muzsnay Zoltán (matematikus)
Cím:	Inverse problem of the calculus of variations on Lie groups / Zoltán Muzsnay, Gerard Thompson
Dátum:	2005
Megjegyzések:	This article studies the inverse problem of the calculus of variations for the special case of the geodesic flow associatedto the canonical symmetric bi-invariant connection of a Lie group. Necessary background on the differentialgeometric structure of the tangent bundle of a manifold as well as the Fröhlicher?Nijenhuis theory of derivations isintroduced briefly. The first obstructions to the inverse problem are considered in general and then as they appearin the special case of the Lie group connection. Thereafter, higher order obstructions are studied in a way that isimpossible in general. As a result a new algebraic condition on the variational multiplier is derived, that involvesthe Nijenhuis torsion of the Jacobi endomorphism. The Euclidean group of the plane is considered as a working exampleof the theory and it is shown that the geodesic system is variational by applying the Cartan?Kähler theorem.The same system is then reconsidered locally and a closed form solution for the variational multiplier is obtained.Finally some more examples are considered that point up the strengths and weaknesses of the theory.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban Variational principle Euler-Lagrange equation Lie group
Megjelenés:	Differential Geometry and its Applications. - 23 : 3 (2005), p. 257-281. -
További szerzők:	Thompson, Gerard
Internet cím:	DOI Intézményi repozitóriumban (DEA) tárolt változat Szerző által megadott URL
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