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arXiv · 2202.04240

Remarks on Exact G$_{2}$-Structures on Compact Manifolds

Aaron Kennon
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Abstract

An important open question in G$_{2}$ geometry concerns whether or not a compact seven-manifold can support an exact G$_{2}$-Structure. Given the significance of this question we initiate a study of exact G$_{2}$-Structures on compact manifolds. We focus on exact G$_2$-Structures subject to no additional constraints but we also consider the relationship between the exact condition and other conditions for closed G$_{2}$-Structures such as the Extremally Ricci-Pinched and Laplacian Soliton conditions.

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Aaron Kennon. 2022-02-09. Remarks on Exact G$_{2}$-Structures on Compact Manifolds. https://arxiv.org/abs/2202.04240

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