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Twistor spinors with zeros. (English) Zbl 0818.53054
A conformal transformation $$f$$ of a Riemannian manifold is essential, if the 1-parameter subgroup generated by $$f$$ is not a group of isometries for any conformally equivalent metric. The main result of the paper deals with the behaviour of the flow generated by $$f$$ near a fixed point. It turns out that the manifold under consideration is conformally flat in a neighborhood of the fixed point. The authors apply this result to the classification of Riemannian manifolds admitting twistor spinors with zeros and with non-vanishing associated vector field. These spaces are conformally flat, a result proved several years ago by K. Habermann under additional curvature assumptions.

##### MSC:
 53C20 Global Riemannian geometry, including pinching 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
##### Keywords:
conformal vector field; spin manifold; twistor spinors
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