Sur le problème inverse du calcul des variations : existence de lagrangiens associés à un spray dans le cas isotrope. (On the inverse problem of the variational calculus: existence of Lagrangians associated with a spray in the isotropic case.)

DOI10.5802/aif.1722zbMath0939.58023OpenAlexW2327740485MaRDI QIDQ1294749

Zoltán Muzsnay, Joseph Grifone

Publication date: 10 August 1999

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1999__49_4_1387_0

zbMATH Keywords

inverse problemvariational calculusEuler-Lagrange equationssectional curvatureconnectionsFinsler spacesoverdetermined systems of partial differential equationsCartan-Kähler theoremsprays

Mathematics Subject Classification ID

Variational principles in infinite-dimensional spaces (58E30) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Linear and affine connections (53B05) Overdetermined systems of PDEs with variable coefficients (35N10)

Related Items (12)

An EDS approach to the inverse problem in the calculus of variations ⋮ The inverse problem for six-dimensional codimension two nilradical lie algebras ⋮ Sprays of weakly isotropic curvature ⋮ Variational connections on Lie groups ⋮ Sprays of isotropic curvature ⋮ A generalization of Szebehely's inverse problem of dynamics ⋮ The inverse problem for Lagrangian systems with certain non-conservative forces ⋮ Thirty years of the inverse problem in the calculus of variations ⋮ Some classes of sprays in projective spray geometry ⋮ The inverse problem of the calculus of variations: The use of geometrical calculus in Douglas’s analysis ⋮ Inverse problem of sprays with scalar curvature ⋮ Inverse problem of the calculus of variations on Lie groups

Cites Work

• The integrability conditions in the inverse problem of the calculus of variations for second-order ordinary differential equations
• Existence theorems for analytic linear partial differential equations
• The inverse problem of the calculus of variations for ordinary differential equations
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