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„Sur l'écart géodésique,” Math. Annalen97 (1926), p. 291–320. Cf. also Levi-Civita, „The Absolute Differential Calculus,” English Translation (1927).
„On the Geometry of Dynamics,” Phil. Trans. Roy. Soc., A,226 (1926), p 31–106. That paper will be referred to as GD. The dynamical problem of „Stability in the action sense,” discussed in GD., Chap. IX, is precisely the geometrical problem of the stability of geodesics in Riemannian space.
G. Vranceanu, „Sur les espaces non holonomes,” Comptes Rendus183 (1926), p. 852–854; „Sur le calcul différentiel absolu pour les variétés non holonomes,” ibid., p. 1083–1085; „Sopra una classe di sistemi anolonomi,” Rend. Acc. Lincei (6)3 (1926), p. 548–553; „Sopra le equazioni del moto di un sistema anolonomo,” ibid.4 (1926), p. 508–511; „Sopra la stabilità geodetica”, ibid.5 (1927), p. 107–110. T. Boggio, „Sullo scostamento geodetico,” Rend. Acc. Lincei (6)4 (1926), p. 255–261. U. Crudeli, „Su lo scostamento geodetico elementare; procedimento di estensione della equazione di Jacobi ad una qualsiasi varietà riemanniana,” Rend. Acc. Lincei (6)5 (1927), p. 248–251. E. Cartan, „Sur l'écart géodésique et quelques notions connexes,” Rend. Acc. Lincei (6)5 (1927), p. 609–613.
„Sopra la stabilità geodetica,” p. 107.
GD., p. 58, Theorem XVII (A).
Cf. Cartan,——loc. cit.„.
It is not necessary that one should occur as a superscript and the other as a subscript.
This rule is not observed in the case of Γ r mn defined in (4. 31).
The present notation is used by Eisenhart, Riemannian Geometry (1926).
GD., p. 54.
Geodesics in non-holonomic geometry have been defined by Vranceanu, Comptes Rendus183 (1926), p. 854, but he has not connected his definition with a variational principle. However it is not difficult to derive his equations from the variational principle here adopted. The curves defined by him are therefore identical with those of the present paper, but the notation is entirely different.
Proc. London Math. Soc. (2)25 (1926), p. 253.
This definition differs from the definition of parallel propagation given by Vranceanu, Comptes Rendus183 (1926), p. 853, which applies only to vectors satisfying the constraints.
Proc. Nat. Acad. Sci.8 (1922), p. 19.
Cf. Proc. London Math. Soc. (2)25 (1926), p. 252.
Math. Annalen97 (1926), p. 315, equation (42).
Cf. GD., equation (9. 21).
GD., p. 58, Theorem XVII (A).
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Synge, J.L. Geodesics in non-holonomic geometry. Math. Ann. 99, 738–751 (1928). https://doi.org/10.1007/BF01459122
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DOI: https://doi.org/10.1007/BF01459122