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arXiv · 2105.11129

Rarita-Schwinger fields on nearly K\"{a}hler manifolds

Soma Ohno·Takuma Tomihisa
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Abstract

We study Rarita-Schwinger fields on 6-dimensional compact strict nearly K\"{a}hler 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 the Rarita-Schwinger fields coincides with the space of the harmonic 3-forms. Applying the same technique to a deformation theory, we also find that the space of the infinitesimal deformations of Killing spinors coincides with the direct sum of a certain eigenspace of the Laplace operator and the space of the Killing spinors.

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Soma Ohno, Takuma Tomihisa. 2021-05-24. Rarita-Schwinger fields on nearly K\"{a}hler manifolds. https://arxiv.org/abs/2105.11129

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