Infinitesimal deformations of Killing spinors on nearly parallel ${\mathrm{G}}_2$-manifolds

Abstract

Manifolds admitting Killing spinors are Einstein manifolds. Thus, a deformation of a Killing spinor entails a deformation of Einstein metrics. In this paper, we study infinitesimal deformations of Killing spinors on nearly parallel ${\mathrm{G}}_2$-manifolds. Since there is a one-to-one correspondence between nearly parallel ${\mathrm{G}}_2$-structures and Killing spinors on 7-dimensional spin manifolds, our results imply that infinitesimal deformations of nearly parallel ${\mathrm{G}}_2$-structures are examined in terms of Killing spinors. Applying the same technique, we identify that the space of the Rarita-Schwinger fields coincides with a subspace of the eigenspace of the Laplacian.

arXiv admin note: text overlap with arXiv:2105.11129