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Hyperbolic complex numbers and nonlinear sigma models

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  1. Antoine, J.-P., and Piette, B. (1986). Classical non-linear sigma models on Grassmannian manifolds of compact or non-compact type, UCL-IPT-86-21.
  2. Borchers, H. J., and Garber, W. D. (1980). Local theory of solutions for theO(2k+1)?-model,Communications in Mathematical Physics,72, 77.
  3. Clifford, W. K. (1968).Mathematical Papers, Chelsea, New York.
  4. Demys, K. (1987). Comment on a paper by Z.-Z. Zhong,Journal of Mathematical Physics,28, 339.
  5. Eichenherr, H., and Forger, M. (1979). On the dual symmetry of the non-linear sigma models,Nuclear Physics B,155, 381.
  6. Eichenherr, H., and Forger, M. (1980). More about non-linear sigma models on symmetric spaces,Nuclear Physics B,164, 528.
  7. Forger, M. (1983). Nonlinear sigma models on symmetric spaces, inNonlinear Partial Differential Operators Quantization Procedures, Springer-Verlag, Berlin.
  8. Fujii, K. (1985). Classical solutions of higher-dimensional nonlinear sigma models,Letters in Mathematical Physics,10, 49?54.
  9. Harnad, J., Saint-Aubin, Y., and Shnider, S. (1984a). Backlund transformations for nonlinear sigma models with values in Riemannian symmetric spaces,Communications in Mathematical Physics,92, 329.
  10. Harnad, J., Saint-Aubin, Y., and Shnider, S. (1984b). The soliton correlation matrix and the reduction problem for integrable systems,Communications in Mathematical Physics,93, 33.
  11. Kunstatter, G., Moffat, J. W., and Malzan, R. (1983). Geometrical interpretation of a generalized theory of gravitation,Journal of Mathematical Physics,24, 886?889.
  12. Lambert, D., and Kibler, M. (1986). An algebraic and geometric approach to nonbijective quadratic transformations, Lycen (Lyon)-8642.
  13. Laurentiev, M., and Chabat, B. (1980).Effets hydrodynamiques et mod�les math�matiques, Mir, Moscow, 1980.
  14. Muses, C. (1970). Invited Lecture, Ames Research Center (NASA), Moffet Field, California.
  15. Nesterenko, V. V. (1987). Nonlinear two-dimensional sigma model with the pseudo-orthogonal symmetry group, Dubna-JINR-E2-82-761.
  16. Piette, B., and Lambert, D. (1987). Generalized Din and Zakrzewski method, UCL, in preparation.
  17. Pohlmeyer, K. (1976). Integrable Hamiltonian systems and interactions through quadratic constraints,Communications in Mathematical Physics,46, 207.
  18. Polubarinov, I. V. (1985). Higher hypercomplex numbers and quantum mechanics, JINR (Dubna)-E2-85-930.
  19. Saint-Aubin, Y. (1982). Backlund transformations and soliton-type solutions for?-models with values in real Grassmannian spaces,Letters in Mathematical Physics,6, 441.
  20. Salingaros, N. (1981). Algebras with three anti commuting elements II. Two algebras over a singular field.Journal of Mathematical Physics,22, 2096?2100.
  21. Wolf, J. A. (1974).Spaces of Constant Curvature, Publish or Perish, Boston.
  22. Yaglom, I. M. (1968).Complex Numbers in Geometry, Academic Press, New Yotk.
  23. Zakharov, V. E., and Mikhalov, A. V. (1978). Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse problem scattering method,Soviet Physics JETP 47, 1017.
  24. Zakrzewski, W. J. (1982). Classical solutions toCP n?1 models and their generalizations, inIntegrable Quantum Field Theory, Springer-Verlag, Berlin, pp. 160?188.
  25. Zakrzewski, W. J. (1984). Classical solutions of two-dimensional Grassmannian?-model,Journal of Geometric Physics,1, 39.
  26. Zhong, Z.-Z. (1984). On the localGL(4, ?) gauge symmetry of hyperbolic complex metrics,Journal of Mathematical Physics,25, 3538?3539.
  27. Zhong, Z.-Z. (1985). On the hyperbolic complex linear symmetry groups and their local guage transformation actions,Journal of Mathematical Physics,26, 404?406.