Year: 2018
Type: preprint
Abstract: The Hodge star mean curvature flow on a 3-dimensional Riemannian or pseudo-Riemannian manifold is a natural nonlinear dispersive curve flow in geometric analysis. A curve flow is integrable if the local differential invariants of a solution to the curve flow evolve according to a soliton equation. In this paper, we show that this flow on $\mathbb{S}^3$ and $\mathbb{H}^3$ are integrable, and describe algebraically explicit solutions to such curve flows. The Cauchy problem of the curve flows on $\mathbb{S}^3$ and $\mathbb{H}^3$ and its Bäcklund transformations follow from this construction.
Source: arXiv (Cornell University)
Author: Liu, Hsiao-Fan
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2785849804