Krupka, Demeter A geometric theory of ordinary first order variational problems in fibered manifolds. I: Critical sections. (English) Zbl 0312.58002 J. Math. Anal. Appl. 49, 180-206 (1975). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 28 Documents MSC: 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 PDF BibTeX XML Cite \textit{D. Krupka}, J. Math. Anal. Appl. 49, 180--206 (1975; Zbl 0312.58002) Full Text: DOI OpenURL References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.