Rarita-Schwinger fields on nearly K\"{a}hler manifolds
Differential Geometry
2021-05-25 v1
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.
Keywords
Cite
@article{arxiv.2105.11129,
title = {Rarita-Schwinger fields on nearly K\"{a}hler manifolds},
author = {Soma Ohno and Takuma Tomihisa},
journal= {arXiv preprint arXiv:2105.11129},
year = {2021}
}