An Integral Formula for a Riemannian Manifold with $k>2$ Singular Distributions

Mathematicians have shown interest in manifolds endowed with several distributions, e.g., webs composed of different regular foliations and multiply warped products, as well as distributions having variable dimensions (e.g., singular Riemannian foliations). In this paper, we extend our previous study of the mixed scalar curvature of two orthogonal singular distributions for the case of $k>2$ singular (or regular) pairwise orthogonal distributions, prove an integral formula with this kind of curvature, and illustrate it by characterizing autoparallel singular distributions.

Algebraic nature of singular Riemannian foliations in spheres

We prove that singular Riemannian foliations in Euclidean spheres can be defined by polynomial equations.