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

Mathematics Subject Classification 53C10 · 53C24 · 53C43For 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 Hermitian and almost contact metric structures.I wish to thank Ilka Agricola for indication of references [4] and [1] and helpful conversations. The author is partially supported by the National Science Center, Poland—Grant Miniatura 2017/01/X/ST1/01724