论文标题
Dirac Bundles的曲折部分
Twistor sections of Dirac bundles
论文作者
论文摘要
Dirac Bundle是Riemannian歧管$ M $上的欧几里得捆绑包，这是一个兼容的左$ C \ ell（m）$ - 模块，并以自然方式与Clifford Action兼容。我们证明了一些消失的定理，并在此框架内介绍了Twistor方程。特别是，我们根据Dirac Operator $ d $和合适的Weitzenböck-type曲率操作员$ \ Mathcal {r} $来展示该方程的解决方案的特征。最后，我们分析了Clifford捆绑包的特殊情况，以证明在球体上存在扭曲器方程的非平凡溶液。
A Dirac bundle is a euclidean bundle over a riemannian manifold $M$ which is a compatible left $C\ell(M)$-module, together with a metric connection also compatible with the Clifford action in a natural way. We prove some vanishing theorems and introduce the twistor equation within this framework. In particular, we exhibit a characterization of solutions for this equation in terms of the Dirac operator $D$ and a suitable Weitzenböck-type curvature operator $\mathcal{R}$. Finally, we analyze the especial case of the Clifford bundle to prove existence of nontrivial solutions of the twistor equation on spheres.
