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.
