abstract

• A Dirac bundle is a euclidean bundle over a riemannian manifold M which is a compatible left Cℓ(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 R. Finally, we analyze the especial case of the Clifford bundle to prove existence of nontrivial solutions of the twistor equation on spheres. © 2020 Elsevier B.V.

authors

• Téllez Téllez Iván

publication date

• 2021-01-01

funding provided via

• 265667; Consejo Nacional de Ciencia y Tecnología, CONACYT  Grant

published in

• Journal of Geometry and Physics  Journal

keywords

• Dirac bundles; Dirac operators; Euclidean bundles; Killing sections; Twistors

Digital Object Identifier (DOI)

• 10.1016/j.geomphys.2020.103957

PubMed ID

start page

end page

volume

• 159

issue