For pairs of singular distributions on Riemannian manifolds, the paper derives a P-divergence theorem and an integral formula relating mixed scalar curvature to second fundamental forms, integrability tensors, and mean curvature vectors.
Blair, Riemannian geometry of contact and symplectic manifolds , Springer, 2010
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An integral formula for a pair of singular distributions
For pairs of singular distributions on Riemannian manifolds, the paper derives a P-divergence theorem and an integral formula relating mixed scalar curvature to second fundamental forms, integrability tensors, and mean curvature vectors.