An integral formula for $G_2$-structures

Abstract

We apply an integral formula obtained by the author for a general $G$--structure to the case of $G=G_2$. We derive an integral formula relating curvatures and some quadratic invariants of the endomorphism induced by the intrinsic torsion. We interpret the formula in certain special cases.

14 pages; minor modifications

References in corpus (2)

• The Srni lectures on non-integrable geometries with torsion
• Notes on the octonions