A geometric theory of ordinary first order variational problems in fibered manifolds. I: Critical sections. (English) Zbl 0312.58002


58A20 Jets in global analysis
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
55R05 Fiber spaces in algebraic topology
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[1] Palais, R.S, Manifolds of sections of fiber bundles and the calculus of variations, (), 195-205, Part I, Chicago, Ill. 1968
[2] Hermann, R, Differential geometry and the calculus of variations, (1968), Academic Press New York and London · Zbl 0219.49023
[3] Hermann, R, Second variation for variational problems in canonical form, Bull. amer. math. soc., 71, 145-149, (1965) · Zbl 0141.10702
[4] Krupka, D, Lagrange theory in fibered manifolds, Rep. math. phys., 2, 121-133, (1971) · Zbl 0219.49022
[5] Krupka, D, On the structure of the Euler mapping, Arch. math. (Brno), 10, (1974), to appear · Zbl 1298.70023
[6] Trautman, A, Invariance of Lagrangian systems, (), 85-99
[7] Trautman, A, Noether equations and conservation laws, Comm. math. phys., 6, 248-261, (1967) · Zbl 0172.27803
[8] Śniatycki, J, On the geometric structure of classical field theory in Lagrangian formulation, (), 475-484 · Zbl 0197.18501
[9] Vanžura, J, Invariants of submanifolds, Czechoslovak math. J., 19, 452-468, (1969) · Zbl 0193.49702
[10] Kuranishi, M, Lectures on involutive systems of partial differential equations, (1967), Publicacoes da Sociedade de Matematica de Sao Paulo Sao Paulo · Zbl 0163.12001
[11] Lepage, Th.H.J; Lepage, Th.H.J, Sur LES champs géodésiques du calcul des variations, Bull. acad. roy. belg. cl. sci. V Sér., Bull. acad. roy. belg. cl. sci. V Sér., 22, 1036, (1936) · Zbl 0016.26201
[12] Boerner, H, Über die legendresche bedingung und die feldtheorien in der variationsrechnung der mehrfachen integral, Math. Z., 46, 720-742, (1940) · JFM 66.0480.03
[13] Krupka, D, On generalized invariant transformations, Rep. math. phys., 5, 353-358, (1974)
[14] Logan, J.D, Generalized invariant variational problems, J. math. anal. appl., 38, 175-186, (1972) · Zbl 0202.11704
[15] Lang, S, Introduction to differentiable manifolds, (1962), Interscience New York and London · Zbl 0103.15101
[16] Sternberg, S, Lectures on differential geometry, (1964), Prentice Hall Englewood Cliffs, NJ · Zbl 0129.13102
[17] KolÁŘ, I, Introduction to the theory of jets (preprint in Czech), ČSAV Brno, (1972), Czechoslovakia
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