Tensor fields defining a tangent bundle structure

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1. [1] C. Itzykson and J.B. Zuber, Quantum Field Theory, McGraw-Hill. N. Y. 1980. L.D. Faddeev and A.A. Slavnov, Gauge Fields. Introduction to Quantum Theory, Benjamin/Cummings, London, 1980. MR585517
2. B.S. De Witt, Quantum Theory of Gravity I: The Canonical Theory. Phys. Rev., t. 160, 1967, p. 1113. Zbl0158.46504
3. B.S. De Witt, Quantum Theory of Gravity II; The manifestely Covariant Theory. Phys. Rev., t. 162, 1967, p. 1195-1239. Zbl0161.46501
4. B.S. De Witt, Quantum Theory of Gravity III ; Applications of Covariant Theory. Phys. Rev., t. 162, 1967, p. 1239-1256. Zbl0161.46501
5. [2] P.A.M. Dirac, Lectures on Quantum Mechanics. Belfer Graduate School of Science Monographs Series n. 2, N.Y. 1964. 
6. E.C.G. Sudarshan and N. Mukunda, Classical Dynamics: A Modern Perspective. Wiley and Sons, N. Y. 1974. Zbl0329.70001MR434047
7. A. Hanson, T. Regge and C. Teitelboim, Constrained Hamiltonian Systems. Accademia Nazionale dei LinceiRoma1976. 
8. [3] L.D. Faddeev, Feynman Integral for Singular Lagrangian. Theor. Math. Phys., t. 1, 1970, p. 1. MR465005
9. [4] R. Abraham and J. Marsden, Foundations of Mechanics. BenjaminReading, Massachussets, 1978. Zbl0393.70001MR515141
10. [5] G. Marmo, E.J. Saletan, A. Simoni and B. Vitale, Symmetry and Reduction of Dynamical Systems. Wiley and Sons, N. Y.1985. Zbl0592.58031MR818988
11. P. Libermann and C.M. Marle, Symplectic Geometry and analitical Mechanics. Zbl0643.53002
12. D. ReidelDordrecht, 1987. 
13. K. Yano and S. Ishimara, Tangent and Cotangent Bundles. Marcel Dekker, 1973. Zbl0262.53024
14. M. Crampin, Tangent Bundle Geometry for Lagrangian Dynamics. J. Phys., t. A16, 1983, p. 3755-3772. Zbl0536.58004MR727054
15. [6] G. Marmo, N. Mukunda and J. Samuel, Dynamics and Symmetry for Constrained Systems; A Geometrical Analysis. La Rivista del Nuovo Cimento, t. 6, 1983, p. 2. MR729476
16. J. Gotay, J. Nester and G. Hinds, Presymplectic Manifolds and the Dirac-Bergman Theory of Constraints. J. Math. Phys., t. 19, 1978, p. 2388. Zbl0418.58010MR506712
17. J. Gotay and J. Nester, Presymplectic Lagrangian Systems I: The Constraint Algorithm and the Equivalence Theorem. Ann. Inst. H. Poincaré, t. 30A, 1979, p. 129-142. Zbl0414.58015MR535369
18. J. Gotay and J. Nester, The Second Order Equation Problem. Ann. Inst. H. Poincaré, t. 32A, 1980, p. 1-13. Zbl0453.58016
19. [7] G. Morandi, C. Ferrario, G. Lo Vecchio, G. Marmo and C. Rubano, The Inverse Problem in the Calculus of Variations and the Geometry of the Tangent Bundle. Naples Preprint, 1987. Zbl1211.58008MR1050526
20. H.P. Kunzle, Canonical Dynamics of Spinning Particles in Gravitational and Electromagnetic Fields. J. Math. Phys., t. 13, 1972, p. 739-744. Zbl0232.70018MR299139
21. F. Cantijn, J.F. Carinena, M. Crampin and L.A. Ibort, Reduction of degenerate Lagrangian Systems. J. Geom. Phys., t. 3, 1986, p. 3. Zbl0621.58020MR894631
22. [8] A.P. Balachandran, G. Marmo, B.S. Skagerstam and A. Stern, Gauge Symmetries and Fibre Bundles. Lecture Notes in Physics, 1988, p. 188. Zbl0525.53065
23. [9] P. Tondeur, Introduction to Lie Groups and Transformation Group. Lecture Notes in Math., n° 7Springer Verlag, 1969. Zbl0198.05001
24. [10] T. Nagano, 1-Forms With the Exterior derivative of Maximal Rank. J. Differential Geometry, t. 2, 1968, p. 253-264. Zbl0172.46903MR239526
25. [11] J. Klein, Structures symplectiques ou J-symplectiques homogènes sur l'espace tangent à une variété. Sympos. Math., t. 14, 1974, p. 181-192. Zbl0306.53037MR388449
26. J. Klein, Proc. IUTAM-ISIMM symposium on modern developments in analytical mechanics. S. Benenti, M. Francaviglia and A. Lichnerowicz eds. Pitagora (Bologna1984). 
27. [12] M. Crampin, Defining Euler-Lagrange Fields in Terms of Almost Tangent Structures. Phys. Lett., t. 95A, 1983, p. 466-468. MR708702
28. [13] M. Crampin and G. Thompson, Affine Bundles and Integrable Almost Tangent Structures. Math. Proc. Camb. Phil. Soc., t. 98, 1985, p. 61-71. Zbl0572.53031MR789719

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