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Nonholonomic conditions

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Literature Cited

  1. V. I. Bliznikas, “Nonholonomic Lie differentiation and linear connections in spaces of support elements,” Liet. Mat. Rinkinys,6, No. 2, 141–208 (1966).

    Google Scholar 

  2. V. I. Bliznikas, “Linear differential-geometric connections of higher order in the space of support elements,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 13–24 (1966).

    Google Scholar 

  3. V. I. Bliznikas, “Finsler spaces and their generalizations,” Itogi Nauki. Algebra. Topologiya. Geometriya, 73–125 (1967, 1969).

  4. V. I. Bliznikas and Z. Yu. Lupeikis, “Geometry of differential equations,” Itogi Nauki. Algebra. Topologiya. Geometriya,11, 209–259 (1974).

    Google Scholar 

  5. V. V. Vagner, “Theory of a composite manifold,” Tr. Sem. Vektorn. Tenzorn. Anal.,8, 11–72 (1950).

    Google Scholar 

  6. R. V. Vosilyus, “Geometry of fibred submanifolds,” Tr. Geometr. Sem. Vses. Inst. Nauchnoi Tekh. Inf.,5, 201–237 (1974).

    Google Scholar 

  7. R. V. Vosilyus, “Formal differentiation in spaces of geometric objects,” Liet. Mat. Rinkinys,15, No. 4, 17–40 (1975).

    Google Scholar 

  8. R. V. Vosilyus, “Generalized linear structures and geometry of submanifolds,” Liet. Mat. Rinkinys,17, No. 4 31–82 (1977).

    Google Scholar 

  9. R. V. Vosilyus, “Geometry of systems of differential equations. I. Normalization of the Fröhlicher-Nuijenhuis theory,” Liet. Mat. Rinkinys,21, No. 2, 67–80 (1981).

    Google Scholar 

  10. R. V. Vosilyus, “Contravariant theory of differential extension in a model of a space with connection,” Itogi Nauki i Tekhniki. Problemy Geom.,14, 101–176 (1983).

    Google Scholar 

  11. G. F. Laptev, “Differential geometry of immersed manifolds,” Trudy Mosk. Mat. O-va,2, 275–382 (1953).

    Google Scholar 

  12. Yu. G. Lumiste, “Theory of connections in bundle spaces,” Itogi Nauki. Algebra. Topologiya. Geometriya, 123–168 (1969, 1971).

  13. Yu. I. Manin, “Holomorphic supergeometry and the Yang-Mills superfield,” Itogi Nauki Tekh. Sov. Probl. Mat. Noveishie Dost,24, 3–78 (1984).

    Google Scholar 

  14. B. N. Shapukov, “Connections on differentiable bundles,” Itogi Nauki Tekh. Probl. Geom.,15, 61–93 (1983).

    Google Scholar 

  15. E. Bompiani, “Le connessioni tensoriall,” Atti Acad. Naz. Linzei,1(5), 478–482 (1946).

    Google Scholar 

  16. E. Cartan, “Les espaces à connexion conforme,” Ann. Soc. Pol. Math.,2, 171–221 (1923).

    Google Scholar 

  17. E. Cartan, “Sur les varietés à connexion projective,” Bull. Soc. Math. France,52, 205–241 (1924).

    Google Scholar 

  18. E. Cartan. “Les groupes d'holonomie des espaces généralises,” Acta Math.,48, 1–42 (1926).

    Google Scholar 

  19. E. B. Christoffel, “Über die Transformation der homogenen Differentialausdrücke zweiten Grades,” J. Reine Angew. Math. (Crelle),70, 46–70 (1896).

    Google Scholar 

  20. C. Ehresmann, “Les prolongements d'une variété differentiable. V. Covariants differentiels et prolongements d'une structure infinitésimale,” C. R. Acad. Sci. Paris,234, 1424–1425 (1952).

    Google Scholar 

  21. S. Hokari, “Die intrinsike Theorie der Geometrie des Systems der partiellen Differentialgleichungen,” Proc. Imp. Acad. Tokyo,16, No. 8, 326–332 (1940).

    Google Scholar 

  22. H. Hombu. “Projektive Transformation eines Systems der gewöhnlichen Differentialgleichungen dritter Ordnung,” Proc. Imp. Acad. Tokyo,13, 187–190 (1937).

    Google Scholar 

  23. R. König, “Beiträge zu einer allgemeinen Mannigfaltigkeitslehre,” Jahresb. Deutsch. Math. Ver.,28, 213–228 (1920).

    Google Scholar 

  24. T. Levi-Civita, “Nozione di parallelismo in una varieta qualungque e consequente specificazione geometrica della curvatura Riemanniana,” Rend. Circ. Math. Palermo,42, 173–205 (1919).

    Google Scholar 

  25. R. Lipschitz, “Untersuchungen in Betreff der ganzen homogenen Funktionen von n Differentialen,” J. Reine Angew. Math. (Crelle),70, 71–102 (1869).

    Google Scholar 

  26. G. Ricci, “Sui parametri gli invarianti delle forme quadratiche differentiale,” Ann. di Math.,11, No. 11, 1–11 (1886).

    Google Scholar 

  27. G. Ricci and T. Levi-Civita, “Methodes de calcul différentiel absolu et leurs applications,” Math. Ann.,54, 125–201 (1901).

    Google Scholar 

  28. J. M. Thomas, “Conformal invariants,” Proc. Nat. Acad. Sci. U.S.A.,12, 389–393 (1925).

    Google Scholar 

  29. T. Y. Thomas, “On the projective and equiprojective geometries of paths,” Proc. Nat. Acad. Sci. U.S.A.,11, No. 4, 199–203 (1925).

    Google Scholar 

  30. H. Weyl, Raum, Zeit, Materie, Berlin (1918).

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Authors
  1. V. I. Bliznikas
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  2. R. Vosylius
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Additional information

Vilnius State Pedagogic Institute. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 27, No. 1, 15–27, January–March, 1987.

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Bliznikas, V.I., Vosylius, R. Nonholonomic conditions. Lith Math J 27, 9–18 (1987). https://doi.org/10.1007/BF00972016

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  • DOI: https://doi.org/10.1007/BF00972016

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