Abstract
On the basis of the generalizations of the Jacobi identity found by the author, some identities satisfied by the curvature and torsion of the covariant differentiation are derived. A kind of the generalized covariant differentiation is proposed and a method of finding some of the identities satisfied by them is given in correspondence to the curvatures concerned. Possible applications to some physical problems are pointed out.
Research partially supported by the Foundation for Scientific Research of Bulgaria under contract Grant No. F 103.
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References
Chevalley, C. (1946) The theory of Lie Groups, vol. I, Princeton Univ. Press, Princeton, ch. IV, §11.
Faith, C. (1973) Algebra: Rings, Modules and Categories, vol. I, Springer Verlag, ch. 1, 3.
Goldstein, H. (1951) Classical Mechanics, Addison-Wesley Press.
Helgason, S. (1978) Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, New York-San Francisco-London, p. 69.
Iliev, B. Z. (1992) “On some generalizations of the Jacobi identity I.”, Bull. Soc. Sci. Lettres Łódź 42, no.21, Série: Recherches sur les déformations 14, no.131, 5–11.
Kobayashi, S. and Nomizu, K. (1963) Foundations of Differential geometry, vol I., Interscience Publishers, New York-London.
Lanczos, C. (1957) “Electricity and general relativity”, Rev. Mod. Phys. 29, no.3, 337–350.
Ławrynowicz, J. (1993) “Special Fueter equations related to the many-particle problem”, Ms.
Nesterenko, V. V. (1989) “Singular Lagrangians with higher derivatives”, J. Phys. A: Math. Gen. 22, no. 10, 1673–1687.
Sattinger, D.H. and Weaver, O.L. (1986) Lie groups and Algebras with Applications to Physics, Geometry and Mechanics, Springer Verlag, Berlin-Heidelberg-New York-Tokyo.
Schafer, R.D. (1963) Introduction to Nonassociative Algebras, Academic Press, New York-London.
Sternberg, S. (1983) Lectures on Differential Geometry, Chelsea Publ. Co., New York, N. Y.
Szczyrba, W. (1981) “A Hamiltonian structure of the interacting gravitational and matter fields”, J. Math. Phys. 22, no.9, 1926–1944.
Weinberg, S. (1972) Gravitation and cosmology, John Wiley & Sons, Inc., New York-London-Sydney-Toronto.
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© 1994 Springer Science+Business Media Dordrecht
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Iliev, B.Z. (1994). Some Generalizations of the Jacobi Identity with Applications to the Curvature- and Torsion-Depending Hamiltonians of Physical Systems. In: Ławrynowicz, J. (eds) Deformations of Mathematical Structures II. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1896-5_7
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DOI: https://doi.org/10.1007/978-94-011-1896-5_7
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