An integral formula for Riemannian $G$-structures with applications to almost hermitian and almost contact structures

Kamil Niedzialomski

Published 2017-06-26Version 1

For a Riemannian $G$-structure, we compute the divergence of the vector field induced by the intrinsic torsion. Applying the Stokes theorem, we obtain the integral formula on a closed oriented Riemannian manifold, which we interpret in certain cases. We focus on almost harmitian and almost contact metric structures.