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

Abstract

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.

24 pages; section on almost contact structures improved

References in corpus (3)

• The Srni lectures on non-integrable geometries with torsion
• Almost Hermitian 6-Manifolds Revisited
• Special almost Hermitian geometry