ON THE GEOMETRY OF STAR-SHAPED CURVES IN Rn

Abstract

. The manifold M of star-shaped curves in R n is considered via the theory of connections on vector bundles, and cyclic D -modules. The appropriate notion of an ‘integral curve’ (i.e. certain admissible deformations) on M is defined, and the resulting space of admissible deformations is classified via iso-spectral flows, which are shown to be described by equations from the n -KdV (Korteweg–de Vries) hierarchy.