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

Aaron Kennon

paper

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

arXiv:2202.04240

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.

19 pages

Remarks on Exact G2​-Structures on Compact Manifolds

Abstract

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