Rarita-Schwinger fields on nearly Kähler manifolds

Abstract

We study Rarita-Schwinger fields on 6-dimensional compact strict nearly Kähler manifolds. In order to investigate them, we clarify the relationship between some differential operators for the Hermitian connection and the Levi-Civita connection. As a result, we show that the space of Rarita-Schwinger fields coincides with the space of harmonic 3-forms. Applying the same technique to deformation theory, we also find that the space of infinitesimal deformations of Killing spinors coincides with the direct sum of a certain eigenspace of the Laplace operator and the space of Killing spinors.