Surveys on Geometry and Integrable SystemsMartin A. Guest, Reiko Miyaoka, Yoshihiro Ohnita 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 |
Contents
BOBENKO Exploring surfaces through methods from | 1 |
Josef DORFMEISTER Generalized Weierstraß representations | 55 |
Atsushi FUJIOKA and Junichi INOGUCHI Timelike surfaces with | 113 |
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Common terms and phrases
algebra associated assume Bonnet bundle called classified CMC-1 surfaces complex computation condition conformal connected consider constant mean curvature construction coordinate corresponding curve defined denote differential dressing ends equation equivalent Example exists extended fact factorization finite fixed flat flows formula frame function Gauss map genus geodesic geometry give given Hamiltonian harmonic maps Hence holds holomorphic Hopf immersion implies integrable integrable systems involution isothermic Lemma linear loop group manifold Math matrix meromorphic metric minimal surfaces Moreover natural normal Note obtain operator pair parameter periodic potential problem Proof properties Proposition prove relation Remark representation respectively satisfies smooth soliton solution space spectral sphere splitting submanifold surfaces symmetric Theorem theory timelike tori transformation vector field