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Integral formulas for a Riemannian manifold with orthogonal distributions

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Haifa, Mount Carmel, 3498838, Haifa, Israel

    Vladimir Rovenski

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  1. Vladimir Rovenski
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Correspondence to Vladimir Rovenski.

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Rovenski, V. Integral formulas for a Riemannian manifold with orthogonal distributions. Ann Glob Anal Geom 61, 69–88 (2022). https://doi.org/10.1007/s10455-021-09804-2

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  • DOI: https://doi.org/10.1007/s10455-021-09804-2

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