Title: Orthogonal foliations on riemannian manifolds,
Abstract: In this work, we find an equation that relates the Ricci curvature of a
riemannian manifold $M$ and the second fundamental forms of two orthogonal
foliations of complementary dimensions, $\mathcal{F}$ and $\mathcal{F}^{\bot}$,
defined on $M$. Using this equation, we show a sufficient condition for the
manifold M to be locally a riemannian product of the leaves of $\mathcal{F}$
and $\mathcal{F}^{\bot}$, if one of the foliations is totally umbilical. We
also prove an integral formula for such foliations.