**Contemporary Mathematics**

Volume: 308;
2002;
349 pp;
Softcover

MSC: Primary 35; 37; 53; 58; 70;

Print ISBN: 978-0-8218-2938-7

Product Code: CONM/308

List Price: $103.00

Individual Member Price: $82.40

**Electronic ISBN: 978-0-8218-7898-9
Product Code: CONM/308.E**

List Price: $103.00

Individual Member Price: $82.40

# Differential Geometry and Integrable Systems

Share this page *Edited by *
*Martin Guest; Reiko Miyaoka; Yoshihiro Ohnita*

Ideas and techniques from the theory of integrable systems are playing an
increasingly important role in geometry. Thanks to the development of tools
from Lie theory, algebraic geometry, symplectic geometry, and topology,
classical problems are investigated more systematically. New problems are also
arising in mathematical physics. A major international conference was held at
the University of Tokyo in July 2000. It brought together scientists in all of
the areas influenced by integrable systems. This book is the first of three
collections of expository and research articles.

This volume focuses on differential geometry. It is remarkable that many
classical objects in surface theory and submanifold theory are described as
integrable systems. Having such a description generally reveals previously
unnoticed symmetries and can lead to surprisingly explicit solutions. Surfaces
of constant curvature in Euclidean space, harmonic maps from surfaces to
symmetric spaces, and analogous structures on higher-dimensional manifolds are
some of the examples that have broadened the horizons of differential geometry,
bringing a rich supply of concrete examples into the theory of integrable
systems.

Many of the articles in this volume are written by prominent researchers and
will serve as introductions to the topics. It is intended for graduate students
and researchers interested in integrable systems and their relations to
differential geometry, topology, algebraic geometry, and physics.

The second volume from this conference, also available from the AMS, is

#### Table of Contents

# Table of Contents

## Differential Geometry and Integrable Systems

- Contents v6 free
- The index of an isolated umbilical point on a surface 118 free
- The Toda equations and equiharmonic maps of surfaces into flag manifolds 1330
- p-harmonic morphisms: the 1 < p < 2 case and some non-trivial examples 2138
- Schwarzian derivatives and flows of surfaces 3956
- Anti-self-dual metrics on Lie groups 6380
- Weierstraβ-type representation of timelike surfaces with constant mean curvature 7794
- A differential-geometric Schottky problem, and minimal surfaces in tori 101118
- Surfaces in 3-space possessing nontrivial deformations which preserve the shape operator 145162
- Hamiltonian stationary Lagrangian surfaces in Hermitian symmetric spaces 161178
- Line congruences and integrable systems 179196
- Factorizations of harmonic maps of surfaces into Lie groups by singular dressing actions 199216
- On submersive p-harmonic morphisms and their stability 205222
- On Kähler-Liouville manifolds 211228
- Minimal surfaces that attain equality in the Chern-Osserman inequality 223240
- Low dimensional manifolds admitting metrics with the same geodesics 229246
- Harmonic maps of finite type into generalized flag manifolds, and twistor fibrations 245262
- Submanifolds associated to Grassmannian systems 271288
- Harmonic cohomology groups of compact symplectic nilmanifolds 287304
- Bonnet pairs in the 3-sphere 297314
- Subspaces in the category of symmetric spaces 305322
- Integral geometry of submanifolds of real dimension two and codimension two in complex projective spaces 315332
- Jacobi fields along harmonic maps 329346
- Denseness of plain constant mean curvature surfaces in dressing orbits 341358

#### Readership

Graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics.