2008/07/22 by Hiroyuki Chihara, Chihara, Hiroyuki · 1 citation
Mathematics · #47G30 #53C44 #58J40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #math.DG #msc:47G30 #msc:53C44 #msc:58J40
paper · pdf · doi:10.48550/arxiv.0807.3395
13 pages, no figure, minor change
openalex publication_date 2008/07/22 · arxiv created 2008/11/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a short-time existence theorem of solutions to the initial value problem for Schroedinger maps of a closed Riemannian manifold to a compact almost Hermitian manifold. The classical energy method cannot work for this problem since the almost complex structure of the target manifold is not supposed to be parallel with respect to the Levi-Civita connection. In other words, a loss of one derivative arises from the covariant derivative of the almost complex structure. To overcome this difficulty, we introduce a bounded pseudodifferential operator acting on sections of the pullback bundle, and essentially eliminate the loss of one derivative from the partial differential equation of the Schroedinger map.