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Book Review

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Book Information:

Author: M. A. Guest
Title: Harmonic maps, loop groups, and integrable systems
Additional book information: London Mathematical Society Student Texts 38, Cambridge Univ. Press, Cambridge, UK, 1997, xiii + 194 pp., ISBN 0-521-58932-0, $14.95, paperback

References [Enhancements On Off] (What's this?)

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  • [2] F. Burstall, D. Ferus, F. Pedit and U. Pinkall, Harmonic tori in symmetric spaces and commuting Hamiltonian systems on loop algebras. Ann. of Math. (2) 138 (1993), no. 1, 173-212. MR 94m:58057
  • [3] F. Burstall and F. Pedit, Harmonic maps via Adler-Kostant-Symes theory. Harmonic maps and integrable systems, 221-272, Aspects Math., E23, Vieweg, Braunschweig, 1994. CMP 94:09
  • [4] F. Burstall and F. Pedit, Dressing orbits of harmonic maps. Duke Math. J. 80 (1995), no. 2, 353-382. MR 97e:58052
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  • [14] K. Pohlmeyer, Integrable Hamiltonian systems and interactions through quadratic constraints, Comm. Math. Phys. 46 (1976), 207-221. MR 53:12299
  • [15] A. Pressley and G. Segal, Loop groups. Oxford Mathematical Monographs. Oxford Science Publications. The Clarendon Press, Oxford University, New York, 1986. MR 88i:22049
  • [16] M. Sato and Y. Sato, Soliton equations as dynamical systems on infinite-dimensional Grassmann manifold. Nonlinear partial differential equations in applied science (Tokyo, 1982), 259-271, North-Holland Math. Stud., 81, North-Holland, Amsterdam-New York, 1983. MR 86m:58072
  • [17] G. Segal and G. Wilson, Loop groups and equations of KdV type, Inst. Hautes Études Sci. Publ. Math. No. 61, (1985), 5-65. MR 87b:58039
  • [18] G. Segal, Loop groups and harmonic maps. Advances in homotopy theory (Cortona, 1988), 153-164, London Math. Soc. Lecture Note Ser., 139, Cambridge Univ. Press, Cambridge, 1989. MR 91m:58043
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Review Information:

Reviewer: Josef Dorfmeister
Affiliation: TU-Muenchen
Journal: Bull. Amer. Math. Soc. 38 (2001), 251-254
MSC (2000): Primary 58E20, 22E67, 37K10
Published electronically: December 27, 2000
Review copyright: © Copyright 2000 American Mathematical Society
American Mathematical Society