Schrödinger flow on Hermitian locally symmetric spaces
type: Item
instance of: scholarly article
title: Schrödinger flow on Hermitian locally symmetric spaces
zbMATH Open document ID: 1032.53057
author: Hongyu Wang
author: Youde Wang
author: Peter Y. H. Pang
published in: Communications in Analysis and Geometry
publication date: 2003-04-07T00:00:00Z
review text: Given a map \(u_0\) from a Riemannian manifold \(M\) into a complete Kähler manifold \(N\), the flow \(u(x,t)\) defined by the Cauchy problem \(\partial_t u = J(u)\tau(u)\) with the initial condition \(u(x,0)=u_0\) is called the Schrödinger flow, where \(\tau(u)\) denotes the tension field of \(u\). This flow has been investigated from various points of view for many years. The authors in this paper consider a slightly generalized tension field by modifying the energy functional by a coupling function and thus the flow is called the inhomogeneous Schrödinger flow. The main theorem asserts the global existence of the inhomogeneous Schrödinger flow for a smooth coupling function with certain general conditions when \(N\) is a complete Hermitian locally symmetric space and \(M\) is the real line or the \(1\)-dimensional sphere. This result generalizes the global existence result shown by \textit{C. L. Terng} and \textit{K. Uhlenbeck} [Surv. Diff. Geom. IV, Int. Press, Boston MA, 315-402 (1998; Zbl 0935.35163)].
Mathematics Subject Classification ID: 53C44
Mathematics Subject Classification ID: 35Q55
zbMATH DE Number: 1893860
zbMATH Keywords: Schrödinger flow
zbMATH Keywords: Hermitian symmetric space
zbMATH Keywords: inverse scattering
zbMATH Keywords: complete integrability
MaRDI profile type: Publication
full work available at URL: cag.2002.v10.n4.a1
OpenAlex ID: W2738331643
DOI: 10.4310/CAG.2002.V10.N4.A1
description: scientific article; zbMATH DE number 1893860