发表机构
Max Planck Institute for Mathematics in the Sciences; Sichuan University（马克斯·普朗克数学科学研究所; 四川大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从闭自旋环面构造映射分量非调和的Dirac-调和映射，证明在非平坦目标曲面上对任意源度量与自旋结构均存在，并给出耦合浸入及曲线判据等结果。
AI 中文摘要
我们从闭自旋环面构造了映射分量非调和的Dirac-调和映射。对于作为目标的闭黎曼曲面，我们证明当目标度量非平坦时，对每个源度量与每个自旋结构均存在这样的解。这些映射可选取为零伦的、处处秩为一的、张力场处处非零且能量无界的。对于严格负曲率的闭定向目标曲面，当源具有平凡自旋结构时，每个同伦类都包含这样的序列。对于其他自旋结构，我们给出了相同构造的相容性条件。添加一个调和圆分量可得到到任意此类曲面与圆的乘积中的耦合浸入。该构造结合了一个自旋子相位（用于抵消移动目标标架的旋转）与沿闭曲线的曲率平衡。对具有给定带符号曲率面积的短环进行能量极小化，可在不对目标作对称性假设的情况下产生所需曲线。其总测地曲率决定了自旋子的周期性。我们还给出了任意目标维数下的曲线判据、对全测地曲面与扭曲积的应用，以及在每个维数至少为二的闭流形上都适用的目标度量的局部选取。
英文摘要
We construct Dirac-harmonic maps from closed spin tori whose map components are not harmonic. For a closed Riemannian surface as target, we prove that such solutions exist for every source metric and every spin structure whenever the target metric is nonflat. The maps can be chosen null-homotopic, of rank one everywhere, with nowhere-vanishing tension and unbounded energy. For a strictly negatively curved closed oriented target surface, every homotopy class contains such a sequence when the source has the trivial spin structure. For the other spin structures we give a compatibility condition for the same construction. Adding a harmonic circle component yields coupled immersions into the product of any such surface with a circle. The construction combines a spinor phase that cancels the rotation of a moving target frame with a curvature balance along a closed curve. Minimizing the energy of short loops with prescribed signed curvature area produces the required curves without any symmetry assumption on the target. Their total geodesic curvature determines the spinor's periodicity. We also give a curve criterion in arbitrary target dimension, applications to totally geodesic surfaces and warped products, and a local choice of target metric that works on every closed manifold of dimension at least two.
