Abstract
We study the interplay between the basic Dirac operator and the transversal Killing and twistor spinors. In order to obtain results for the general Riemannian foliations with bundle-like metric, we consider transversal Killing spinors that appear as natural extension of the harmonic spinors associated with the basic Dirac operator. In the case of foliations with basic-harmonic mean curvature, it turns out that this type of spinors coincide with the standard definition. We obtain the corresponding version of classical results on closed Riemannian manifold with spin structure, and extending some previous results.
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