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Journal of Mathematical Physics / Volume 32 / Issue 1

J. Math. Phys. 32, 234 (1991); http://dx.doi.org/10.1063/1.529123 (5 pages)

Affine collineations in Riemannian spaces

Sergio A. Hojman1 and Darío Núñez2

1Center for Relativity and Department of Physics, The University of Texas at Austin, Austin, Texas 78712‐1081
2Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. Postal 70‐543, 04510 México, D. F., Mexico

(Received 16 February 1990; accepted 8 August 1990)

Sufficient conditions on the Christoffel symbols and metric tensors to insure the existence of affine collineations in Riemann spaces are obtained. A proof of the group property of affine collineations is given. Several examples of physically relevant Riemannian spaces admitting affine collineations are presented and the constants of motion are constructed.

KEYWORDS and PACS

Keywords

RIEMANN SPACE, EQUATIONS OF MOTION, SYMMETRY GROUPS, TRANSFORMATIONS, GEODESICS, DIFFERENTIAL EQUATIONS, LAGRANGIAN FUNCTION, PERTURBATION THEORY, METRICS, TENSORS

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.529123

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

For access to fully linked references, you need to log in.
    G. H. Katzin and J. Levine, J. Math. Phys. 22, 1878 (1981JMAPAQ000022000009001878000001), and references therein.

    S. Hojman, L. Núñez, A. Patiño, and H. Rago, J. Math. Phys. 27, 281 (1986JMAPAQ000027000001000281000001).

    M. L. Bedran and B. Lesche, J. Math. Phys. 27, 2360 (1986JMAPAQ000027000009002360000001).

    W. Oevel, B. Fuchssteiner, W. Zhang, and O. Ragnisco, J. Math. Phys. 30, 2664 (1989JMAPAQ000030000011002664000001).



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