edited by Martin Guest (Tokyo Metropolitan University, Japan) , Reiko Miyaoka (Tohoku University, Japan) , & Yoshihiro Ohnita (Osaka City University, Japan)

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 3-folds) 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.

Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

• Exploring Surfaces Through Methods from the Theory of Integrable Systems: The Bonnet Problem (A I Bobenko)
• Generalized Weierstraβ Representations of Surfaces (J Dorfmeister)
• Timelike Surfaces with Harmonic Inverse Mean Curvature (A Fujioka & J-i Inoguchi)
• Darboux Transformations and Generalized Self-Dual Yang–Mills Flows (C Gu)
• From CMC Surfaces to Hamiltonian Stationary Lagrangian Surfaces (F Hélein & P Romon)
• Special Lagrangian 3-Folds and Integrable Systems (D Joyce)
• Quantum Product, Topological Recursion Relations, and the Virasoro Conjecture (X Liu)
• A Generalized Weierstrass Representation for a Submanifold S in Eⁿ Arising from the Submanifold Dirac Operator (S Matsutani)
• Harmonic Tori and Their Spectral Data (I McIntosh)
• Isoparametric Geometry and Related Fields (R Miyaoka)
• Kähler Ricci Solitons (H Pedersen)
• Period Problems for Mean Curvature One Surfaces in H³ (with Applications to Surfaces of Low Total Curvature) (W Rossman, M Umehara & K Yamada)
• Geometries and Symmetries of Soliton Equations and Integrable Elliptic Equations (C-L Terng)
• A-Integrability of Geodesic Flows and Geodesic Equivalence (P Topalov)