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Integral formulas for a Riemannian manifold with orthogonal distributions
Annals of Global Analysis and Geometry  (IF0.846),  Pub Date : 2021-10-01, DOI: 10.1007/s10455-021-09804-2
Rovenski, Vladimir

In this article, we introduce and study a new structure on a Riemannian manifold: a distribution represented as the sum of k > 2 pairwise orthogonal distributions. We define the mixed scalar curvature of this structure and prove integral formulas generalizing classical and recent results on foliations and distributions generating the tangent bundle of a manifold. Examples with one-dimensional distributions, paracontact manifolds, hypersurfaces in space forms, etc., illustrate the results.