Geodesic
Theory of fields of extremals for multiple integrals
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 66 (2011) no. 4, pp. 733-765

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A general theory unifying and generalizing the field theories for multiple integrals due to Weyl and Carathéodory is developed. Generalizations of the Legendre, Weyl, and Carathéodory transforms are introduced, as well as the associated connection and curvature on the fibre bundle underlying the multiple integrals. Bibliography: 33 titles.
Keywords: field of extremals, Weierstrass function, connection and curvature on fibre bundles, covariant differentiation.
Mots-clés : Legendre transform 
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     author = {M. I. Zelikin},
     title = {Theory of fields of extremals for multiple integrals},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {733--765},
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     volume = {66},
     number = {4},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2011_66_4_a1/}
}
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M. I. Zelikin. Theory of fields of extremals for multiple integrals. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 66 (2011) no. 4, pp. 733-765. http://geodesic.mathdoc.fr/item/RM_2011_66_4_a1/