Geodesic
The geometry of analytic jets
Sbornik. Mathematics, Tome 53 (1986) no. 2, pp. 367-383 
V. V. Zharinov. The geometry of analytic jets. Sbornik. Mathematics, Tome 53 (1986) no. 2, pp. 367-383. http://geodesic.mathdoc.fr/item/SM_1986_53_2_a4/
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     title = {The geometry of analytic jets},
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     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1986_53_2_a4/}
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The author studies jet manifolds in the real-analytic class, and shows that in this case they are stratified into Cartan submanifolds, which leads to further geometric properties of maps and Lie-Bäcklund fields and topological properties of differential equations. Bibliography: 9 titles.

[1] Lie S., Engel F., Teorie der Transformationsgruppen, Bd. 1–3, Teubner, Leipzig, 1886, 1890, 1893

[2] Kartan E., Vneshnie differentsialnye sistemy i ikh geometricheskie prilozheniya, MGU, M., 1962

[3] Kuranishi M. On E., “Cartan's prolongations theorem of exterior differential systems”, Amer. J. Math., 79:1 (1957), 1–47 | DOI | MR | Zbl

[4] Ovsyannikov L. V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR

[5] Ibragimov N. Kh., Gruppy preobrazovanii v matematicheskoi fizike, Nauka, M., 1983 | MR

[6] Vinogradov A. M., Geometriya nelineinykh differentsialnykh uravnenii, Itogi nauki i tekhniki. Problemy geometrii, 11, VINITI, M., 1980 | MR | Zbl

[7] Tsujishita T., “On variation bicomplexes associated to differential equations”, Osaka J. Math., 19:2 (1982), 311–363 | MR | Zbl

[8] Burbaki N., Differentsiruemye i analiticheskie mnogoobraziya, Mir, M., 1975 | MR

[9] Vinogradov A. M., “Odna spektralnaya posledovatelnost, svyazannaya s nelineinym differentsialnym uravneniem, i algebro-geometricheskie osnovaniya lagranzhevoi teorii polya so svyazyami”, DAN SSSR, 238:5 (1978), 1028–1031 | MR | Zbl