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Book Review

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Book Information

Author(s): 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, $29.95, 3-7643-6576-5

References:

[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

Additional Information:

Reviewer(s):
Robert M. Hardt
Affiliation: Rice University
Email: hardt@rice.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 40 (2003), 121-123.

MSC (2000): Primary 53C42, 70H06; Secondary 53C43, 53C28, 53C35
DOI: 10.1090/S0273-0979-02-00958-8
PII: S 0273-0979(02)00958-8
Posted: October 16, 2002
Copyright of article: Copyright 2002, American Mathematical Society

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