On the geometry of star-shaped curves in ${\mathbb{R}}^n$

Abstract

The manifold $\mathcal{M}$ of star-shaped curves in ${\mathbb{R}}^n$ is considered via the theory of connections on vector bundles, and cyclic $\mathcal{D}$-modules. The appropriate notion of an "integral curve" (i.e. certain admissible deformations) on $\mathcal{M}$ 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 hierarchy.

accepted for publication in Kyushu J. Math

References in corpus (3)

• Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarchy
• Multi-Hamiltonian Structures on Spaces of Closed Equicentroaffine Plane Curves Associated to Higher KdV Flows
• N-dimension Central Affine Curve Flows