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References
H. Akbar-Zadeh, Champs de vecteurs projectifs sur le fibré unitaire, J. Math. pares et appl. 65 (1986), 47–79.
M. Crampin, On the differential geometry of the Euler-Lagrange equations, and the inverse problem of Lagrangian dynamics, J. Phys. A 14 (1981), 2567–2575.
M. Crampin, Tangent bundle geometry for Lagrangian dynamics, J. Phys. A 16 (1983), 3755–3772.
M. Crampin and F. A. E. Pirani, Applicable differential geometry, Cambridge University Press, Cambridge, 1986.
J. Grifone, Structure presque tangente et connexions I., Ann. Inst. Fourier (Grenoble) 22 (1972) 1, 287–334.
J. Grifone, Structure presque tangente et connexions II., Ann. Inst. Fourier (Grenoble) 22 (1972) 3, 291–338.
J. Klein and A. Voutier, Formes extérieures génératrices de sprays, Ann. Inst. Fourier (Grenoble) 18 (1968) 1, 241–260.
S. Lang, Fundamentals of differential geometry, Springer-Verlag, Berlin, 1999.
R. L. Lovas, Lie derivatives and Killing vector fields in Finsler geometry, Proc. Non-Euclidean Geometry in Modern Physics, 2002, 35–50.
E. MartÍnez, J. F. CariÑena and W. Sarlet, Derivations of differential forms along the tangent bundle projection, Diff. Geom. Appl. 2 (1992), 17–43.
M. Matsumoto, Theory of extended point transformations of Finsler spaces I., Tensor (N.S.) 45 (1987), 109–115.
M. Matsumoto, Theory of extended point transformations of Finsler spaces II., Tensor (N.S.) 47 (1988), 203–214.
B. O'Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, New York, 1983.
W. A. Poor, Differential geometric structures, McGraw-Hill, New York, 1981.
L. del Riego and P. E. Parker, Generalized Sprays and Nonlinear Connections, arXiv:math.DG/0304067 v1.
Z. Shen, Differential Geometry of Spray and Finsler Spaces, Kluwer Academic Publishers, Dordrecht, 2001.
J. Szilasi, A setting for spray and Finsler geometry, in: Handbook of Finsler geometry, Vol. 2, ed. by P. L. Antonelli, Kluwer Academic Publishers, Dordrecht, 2003.
J. Szilasi and Á. GyŐry, A generalization of a theorem of H. Weyl, Rep. Math. Phys. 53 (2004), 261–273.
J. Szilasi and Sz. VattamÁny, On the projective geometry of sprays, Diff. Geom. Appl. 13 (2000), 95–118.
J. Szilasi and Sz. VattamÁny, On the Finsler-metrizabilities of spray manifolds, Period. Math. Hungar. 44 (2002), 81–100.
A. A. Tamim, Infinitesimal transformations in Finsler geometry, Afrika Math. J. 3 (1990).
M. E. Taylor, Partial differential equations, I. Basic theory, Applied Mathematical Sciences, Vol. 115, Springer-Verlag, Berlin, 1996.
K. Yano, The theory of Lie derivatives and its applications, North-Holland, Amsterdam, 1957.
Nabil L. Youssef, Semi-projective changes, Tensor (N.S.) 55 (1994), 131–141.
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Lovas, R.L. Affine and projective vector fields on spray manifolds. Periodica Mathematica Hungarica 48, 165–179 (2004). https://doi.org/10.1023/B:MAHU.0000038973.18653.2e
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DOI: https://doi.org/10.1023/B:MAHU.0000038973.18653.2e