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Twistor sections of Dirac bundles
Journal of Geometry and Physics ( IF 1.6 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.geomphys.2020.103957
Sergio A.H. Cardona , Pedro Solórzano , Iván Téllez

Abstract A Dirac bundle is a euclidean bundle over a riemannian manifold M which is a compatible left C l ( 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 Weitzenbock-type curvature operator R . Finally, we analyze the especial case of the Clifford bundle to prove existence of nontrivial solutions of the twistor equation on spheres.

中文翻译:

狄拉克丛的扭曲部分

摘要 狄拉克丛是黎曼流形 M 上的欧几里得丛,它是一个兼容的左 C l ( M ) -模,以及一个度量连接,也以自然的方式与克利福德作用兼容。我们证明了一些消失定理,并在这个框架内引入了扭曲方程。特别是,我们根据狄拉克算子 D 和合适的韦岑博克型曲率算子 R 展示了该方程解的特征。最后,我们分析了 Clifford 丛的特殊情况,以证明球体上扭曲方程的非平凡解的存在性。
更新日期:2021-01-01
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