Mathematical Sciences: Submanifold Geometry and Integrable Systems

小行星9626130 建议的研究在于微分几何中的子流形理论领域。研究者计划研究具有简单焦点结构的完备黎曼流形的子流形。特别是，她感兴趣的是检查子流形与恒定的焦点半径在紧凑的黎曼流形和紧张浸入到完整的黎曼流形。此外，研究者将与K.可积哈密顿系统及其在调和映射和等距浸入中的应用。 子流形理论是几何学中最古老的领域之一。最初的动机来自于空间中的曲面，在本世纪之前，人们做了大量的工作来构造满足某些特殊性质的曲面，其中许多都与曲率有关。拟议的研究旨在深入研究这些特殊的性质，使用现代技术：表面与一个简单的焦点结构，表面承认'Bianchi-Backlund'变换。

9626130 Terng The proposed research lies in the area of submanifold theory in differential geometry. The investigator plans to study submanifolds of complete Riemannian manifolds that have simple focal structures. In particular, she is interested in examining submanifolds with constant focal radii in compact Riemannian manifolds and taut immersions into complete Riemannian manifolds. In addition, the investigator is to engage in a collaborative project with K. Uhlenbeck on integrable Hamiltonian systems and their applications to harmonic maps and isometric immersions. Submanifold theory is a vast and one of the oldest areas in geometry. Original motivation comes from surfaces in space, where a great deal of work was done prior to this century on constructing surfaces satisfying certain special properties, many of them having to do with curvature. The proposed research aims to delve into two of these special properties using modern techniques: surfaces with a simple focal structure, and surfaces admitting 'Bianchi-Backlund' transformations.