通过特征旋量实现三维流形的无散度标架
Divergence-free framings of three-manifolds via eigenspinors
AI总结：
本文利用三维特征旋量的几何性质（受Seiberg-Witten理论启发），为闭可定向三维流形存在线性无关的无散度向量场提供了另一种证明，并进一步证明了在任意Riemannian度量下可找到处处正交且等长的无散度向量场。
摘要：
Gromov利用凸积分证明了任何配备体积形式的闭可定向三维流形都存在三个在每点线性无关的无散度向量场。我们利用三维特征旋量的几何性质，提供了该结论的另一种证明（受Seiberg-Witten理论启发）。事实上，我们的证明表明，对于任意Riemannian度量，都能找到三个无散度向量场，使得它们在每点正交且具有相同的非零长度。
英文摘要：
Gromov used convex integration to prove that any closed orientable three-manifold equipped with a volume form admits three divergence-free vector fields which are linearly independent at every point. We provide an alternative proof of this (inspired by Seiberg-Witten theory) using geometric properties of eigenspinors in three dimensions. In fact, our proof shows that for any Riemannian metric, one can find three divergence-free vector fields such that at every point they are orthogonal and have the same non-zero length.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
