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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2007.02497 |
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Table of Contents:
- We study the deformation theory of nearly $\mathrm{G}_2$ manifolds. These are seven dimensional manifolds admitting real Killing spinors. We show that the infinitesimal deformations of nearly $\mathrm{G}_2$ structures are obstructed in general. Explicitly, we prove that the infinitesimal deformations of the homogeneous nearly $\mathrm{G}_2$ structure on the Aloff--Wallach space are all obstructed to second order. We also completely describe the cohomology of nearly $\mathrm{G}_2$ manifolds.