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 | 55 |
Atsushi FUJIOKA and Junichi INOGUCHI Timelike surfaces with | 113 |
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Common terms and phrases
3-space affine Bonnet pairs Bonnet surfaces bundle catenoid CMC-1 surfaces coefficient condition conformal constant mean curvature construction Corollary corresponding d₁ defined denote Dirac operator do² Dorfmeister elliptic Example exists extended frame finite type flat formula function Gauss map Gauss-Codazzi equations genus geodesically equivalent Geom given Hamiltonian stationary harmonic maps Hence holomorphic Hopf differential hypersurfaces implies integrable systems involution isoparametric hypersurfaces Kähler Lagrangian submanifolds Lax pair Lemma Lie algebra linear loop group manifold Math matrix Maurer-Cartan form mean curvature surfaces meromorphic metric g minimal surfaces obtain parameter Pedit Proof Proposition representation Riemann surface satisfies smooth soliton solution special Lagrangian spectral curve subgroup surfaces in R³ symmetric space TA(ƒ Theorem theory THIMC surfaces timelike timelike surface Toda lattice tori transformation U₁ umbilic points vector field Virasoro conjecture Weierstrass