The star mean curvature flow on 3-sphere and hyperbolic 3-space

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Title:	The star mean curvature flow on 3-sphere and hyperbolic 3-space
Authors:	Liu, Hsiao-Fan
Keywords:	moving frames;Hodge star MCF;Gross–Pitaevskii equation;periodic Cauchy problems;Bäcklund transformation
Date:	2020-06
Issue Date:	2021-08-20 12:11:20 (UTC+8)
Abstract:	The Hodge star mean curvature flow on a 3‑dimensional Riemannian or pseudo-Riemannian manifold is one of nonlinear dispersive curve flows in geometric analysis. Such a curve flow is integrable as its local differential invariants of a solution to the curve flow evolve according to a soliton equation. In this paper, we show that these flows on a 3‑sphere and 3‑dimensional hyperbolic space are integrable, and describe algebraically explicit solutions to such curve flows. Solutions to the (periodic) Cauchy problems of such curve flows on a 3‑sphere and 3‑dimensional hyperbolic space and its Bäcklund transformations follow from this construction.
Relation:	Asian Journal of Mathematics 24(3), p.483–500
DOI:	10.4310/AJM.2020.v24.n3.a5
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

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