  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.
