Advanced Studies in Pure Mathematics 2008; 510 pp; hardcover Volume: 51 ISBN10: 4931469469 ISBN13: 9784931469464 List Price: US$76 Member Price: US$60.80 Order Code: ASPM/51
 The articles in this volume provide a panoramic view of the role of geometry in integrable systems, firmly rooted in surface theory but currently branching out in all directions. The longer articles by Bobenko (the Bonnet problem), Dorfmeister (the generalized Weierstrass representation), Joyce (special Lagrangian 3folds) and Terng (geometry of soliton equations) are substantial surveys of several aspects of the subject. The shorter ones indicate more briefly how the classical ideas have spread throughout differential geometry, symplectic geometry, algebraic geometry, and theoretical physics. Volumes in this series are freely available electronically 5 years postpublication. Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. Readership Graduate students and research mathematicians interested in mathematical physics. Table of Contents  A. I. Bobenko  Exploring surfaces through methods from the theory of integrable systems: The Bonnet problem
 J. Dorfmeister  Generalized Weierstraß representations of surfaces
 A. Fujioka and J. Inoguchi  Timelike surfaces with harmonic inverse mean curvature
 C. Gu  Darboux transformations and generalized selfdual YangMills flows
 F. Hélein and P. Romon  From CMC surfaces to Hamiltonian stationary Lagrangian surfaces
 D. Joyce  Special Lagrangian 3folds and integrable systems
 X. Liu  Quantum product, topological recursion relations, and the Virasoro conjecture
 S. Matsutani  A generalized Weierstrass representation for a submanifold \(S\) in \(\mathbb{E}^n\) arising from the submanifold Dirac operator
 I. McIntosh  Harmonic tori and their spectral data
 R. Miyaoka  Isoparametric geometry and related fields
 H. Pedersen  Kähler Ricci solitons
 W. Rossman, M. Umehara, and K. Yamada  Period problems for mean curvature one surfaces in \(H^3\) (with applications to surfaces of low total curvature)
 C.L. Terng  Geometries and symmetries of soliton equations and integrable elliptic equations
 P. Topalov  Aintegrability of geodesic flows and geodesic equivalence
