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Book Review

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Book Information:

Author: Frédéric Hélein
Title: Constant mean curvature surfaces, harmonic maps and integrable systems
Additional book information: Lectures in Mathematics, ETH Zürich, Birkhäuser, Basel-- Boston--Berlin, 2000, xii+227 pp., ISBN 3-7643-6576-5, $29.95

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

  • [A] U. Abresch: Constant mean curvature tori in terms of elliptic functions. J. Reine Angew. Math. 374 (1987), 169-192. MR 88e:53006
  • [BR] F. Burstall and J.H. Rawnsley: Twistor Theory for Riemannian Symmetric Spaces. Lecture Notes in Math. 1424 Springer-Verlag, Berlin, 1990. MR 91m:58039
  • [G] M. Guest: Harmonic Maps, Loop Groups, and Integrable Systems. London Mathematical Society Student Texts, 38 Cambridge University Press, Cambridge, 1997. MR 99g:58036
  • [DPW] J. Dorfmeister, F. Pedit, and H. Wu: Weierstrass type representation of harmonic maps into symmetric spaces. Comm. Anal. Geom. 6(1998), no. 4, 633-668. MR 2000d:53099
  • [FPPS] D. Ferus, F. Pedit, U. Pinkhall and I. Sterling: Minimal tori in $S\sp4$. J. Reine Angew. Math. 429 (1992), 1-47. MR 93h:53008
  • [FW] A. Fordy and J. Wood: Harmonic Maps and Integrable Systems. Aspects of Mathematics E23 Cambridge University Press, Verweg, 1994, see also http://www.amst.leeds.ac.uk/Pure/staff/wood/FordyWood. MR 95m:58047
  • [H] H. Hopf: Über Flächen mit einer Relation zwischen den Hauptkrümmungen. Math. Nachr. 4 (1951). 232-249. MR 12:634f
  • [K] N. Kapouleas: Compact constant mean curvature surfaces in Euclidean three-space. J. Differential Geom. 33 (1991), no. 3, 683-715. MR 93a:53007b
  • [PS] U. Pinkall and I. Sterling: On the classification of constant mean curvature tori. Ann. of Math. (2) 130 (1989), no. 2, 407-451. MR 91b:53009
  • [RV] E. Ruh and J. Vilms: The tension field of the Gauss map. Trans. Amer. Math. Soc. 149 1970 569-573. MR 41:4400
  • [W] H. Wente: Counterexample to a conjecture of H. Hopf. Pacific J. Math. 121 (1986), no. 1, 193-243. MR 87d:53013

Review Information:

Reviewer: Robert M. Hardt
Affiliation: Rice University
Email: hardt@rice.edu
Journal: Bull. Amer. Math. Soc. 40 (2003), 121-123
MSC (2000): Primary 53C42, 70H06; Secondary 53C43, 53C28, 53C35
Published electronically: October 16, 2002
Review copyright: © Copyright 2002 American Mathematical Society
American Mathematical Society