[1] S. J. Aldersley, G. W. Horndeski:
Conformally invariant tensorial concomitants of a pseudo-Riemannian metric. Utilitas Math. 17 (1980), 197-223.
MR 0583141 |
Zbl 0441.53011
[2] I. M. Anderson:
On the structure of divergence-free tensors. J. Math. Phys. 19 (1978), 2570-2575.
MR 0512978 |
Zbl 0429.53048
[3] I. M. Anderson:
Tensorial Euler-Lagrange expressions and conservation laws. Aequationes Math. 17 (1978), 255-291.
MR 0493675 |
Zbl 0418.49041
[4] I. M. Anderson:
Natural variational principles on Riemannian manifolds. Annals of Math. 120 (1984), 329-370.
MR 0763910 |
Zbl 0565.58019
[5] I. M. Anderson:
The variational bicomplex. (to appear).
Zbl 0881.35069
[6] I. M. Anderson: The minimal order solution to the inverse problem. (to appear).
[7] I. M. Anderson: Natural differential operators on the variational bicomplex. (to appear).
[8] I. M. Anderson, T. Duchamp:
On the existence of global variational principles. Amer. J. Math. 102 (1980), 781-868.
MR 0590637 |
Zbl 0454.58021
[9] I. M. Anderson, T. Duchamp:
Variational principles for second order quasi-linear scalar equations. J. Diff. Eqs. 51 (1984), 1-47.
MR 0727029 |
Zbl 0533.49010
[10] D. E. Betounes:
Extensions of the classical Cartan form. Phys. Rev. D 29 (1984), 599-606.
MR 0734285
[11] K. S. Cheng, W. T. Ni:
Conditions for the local existence of metric in a generic affine manifold. Math. Proc. Camb. Phil. Soc. 87 (1980), 527-534.
MR 0556932 |
Zbl 0442.53020
[12] S. S. Chern, J. Simons:
Characteristic forms and geometric invariants. Annals of Math. 99 (1974), 48-69.
MR 0353327 |
Zbl 0283.53036
[14] V. V. Dodonov V. I. Man'ko, V. D. Skarzhinsky:
The inverse problem of the variational calculus and the nonuniqueness of the quantization of classical systems. Hadronic J. 4 (1981), 1734-1803.
MR 0632443
[15] V. V. Dodonov V. I. Man'ko, V. D. Skarzhinsky:
Classically equivalent Hamiltonians and ambiguities of quantization: a particle in a magnetic field. Il Nuovo Cimento 69B (1982), 185-205.
MR 0669159
[16] J. Douglas:
Solution to the inverse problem of the calculus of variations. Trans. Amer. Math. Soc. 50 (1941), 71-128.
MR 0004740
[17] M. Ferraris:
Fibered connections and Global Poincaré-Cartan forms in higher-order Calculus of Variations. in "Proc. of the Conference on Differential Geometry and its Applications, Nové Město na Moravě, Vol. II. Applications", Univerzita Karlova, Praga, 1984, pp. 61-91.
MR 0793200 |
Zbl 0564.53013
[18] V. N. Gusyatnikova A. M. Vinogradov V. A. Yumaguzhin:
Secondary differential operators. J. Geom. Phys. 2 (1985), 23-65.
MR 0845467
[19] M. Henneaux:
Equations of motions, commutation relations and ambiguities in the Lagrangian formalism. Ann. Phys. 140 (1982), 45-64.
MR 0660925
[20] M. Henneaux, L. C. Shepley:
Lagrangians for spherically symmetric potentials. J. Math. Phys. 23 (1982), 2101-2104.
MR 0680007 |
Zbl 0507.70022
[21] M. Henneaux:
On the inverse problem of the calculus of variations in field theory. J. Phys. A: Math. Gen. 17 (1984), 75-85.
MR 0734109 |
Zbl 0557.70019
[22] S. Hojman, H. Harleston:
Equivalent Lagrangians: Multidimensional case. J. Math. Physics 22 (1981), 1414-1419.
MR 0626131 |
Zbl 0522.70024
[23] G. W. Horndeski:
Differential operators associated with the Euler-Lagrange operator. Tensor 28 (1974), 303-318.
MR 0356143 |
Zbl 0289.49045
[24] J. Klein:
Geometry of sprays. Lagrangian case. Principle of least curvature. in "Proc. IUTAM-ISIMM Symposium on Modern Developments in Analytical Mechanics, Vol. 1", (Benenti, Francavigilia, Lichnerowicz, eds.), Atti dela Accademia delle Scienze di Torino, 1983, pp. 177-196.
MR 0773487 |
Zbl 0566.58012
[25] I. Kolář:
A geometrical version of the higher order Hamilton formalism in fibered manifolds. J. Geom. Phys. 1 (1984), 127-137.
MR 0794983
[26] L. Littlejohn:
On the classification of differential equations having orthogonal polynomial solutions. Annali di Mathematica pure ed applicata 138 (1984), 35-53.
MR 0779537 |
Zbl 0571.34003
[27] D. Lovelock:
The Einstein tensor and its generalizations. J. Math. Physics 12 (1971), 498-501.
MR 0275835 |
Zbl 0213.48801
[28] J. M. Masqué:
Poincaré-Cartan forms in higher order variational calculus on fibred manifolds. Revista Matematica Iberoamericana 1 (1985), 85-126.
MR 0850411
[29] P. J. Olver:
Applications of Lie Groups to Differential Equations. Springer-Verlag, New York, 1986.
MR 0836734 |
Zbl 0588.22001
[30] P. J. Olver: Darboux's theorem for Hamiltonian differential operators. (to appear).
[31] H. Rund:
A Cartan form for the field theory of Carathéodory in the calculus of variations. in "Lecture Notes in Pure and Applied Mathematics No. 100: Differential Geometry, Calculus of Variations, and Their Applications", G. M. Rassias and T. M. Rassias (eds), Marcel Dekker, New York, 1985, pp. 455-470.
MR 0822534 |
Zbl 0578.49025
[32] W. Sarlet:
Symmetries and alternative Lagrangians in higher-order mechanics. Phys. Lett. A 108 (1985), 14-18.
MR 0786789
[33] W. Sarlet F. Cantrijin, M. Crampin:
A new look at second-order equations and Lagrangian mechanics. J. Phys. A: Math. Gen. 17 (1984), 1999-2009.
MR 0763792
[34] F. Takens:
Symmetries, conservation laws and variational principles. in "Lecture Notes in Mathematics No. 597", Springer-Verlag, New York, 1977, pp. 581-603.
MR 0650304 |
Zbl 0368.49019
[35] F. Takens:
A global version of the inverse problem to the calculus of variations. J. Diff. Geom. 14 (1979), 543-562.
MR 0600611
[36] G. Thompson:
Second order equation fields and the inverse problem of Lagrangian dynamics. (to appear).
MR 0917639 |
Zbl 0638.70013
[37] E. Tonti:
Inverse problem: Its general solution. in "Lecture Notes in Pure and Applied Mathematics No. 100: Differential Geometry, Calculus of Variations and Their Applications", Marcel Decker, New York, 1985, pp. 497-510.
MR 0822537 |
Zbl 0583.49010
[38] T. Tsujishita:
On variation bicomplexes associated to differential equations. Osaka J. Math. 19 (1982), 311-363.
MR 0667492 |
Zbl 0524.58041
[39] W. M. Tulczyjew:
The Euler-Lagrange resolution. in "Lecture Notes in Mathematics No. 836," Springer-Verlag, New York, 1980, pp. 22-48.
MR 0607685 |
Zbl 0456.58012
[40] A. M. Vinogradov: On the algebra-geometric foundation of Lagrangian field theory. Sov. Math. Dokl. 18 (1977), 1200-1204.
[41] A. M. Vinogradov:
The C-spectral sequence, Lagrangian formalism and conservation laws I, II. J. Math. Anal. Appl. 100 (1984), 1-129.
MR 0739952
[42] E. Witten:
Global aspects of current algebra. Nucl. Phys. B223 (1983), 422-432.
MR 0717915