  We study curvature invariants of a sub-Riemannian manifold (i.e., a manifold
with a Riemannian metric on a non-holonomic distribution) related to mutual
curvature of several pairwise orthogonal subspaces of the distribution, and
prove geometrical inequalities for a sub-Riemannian submanifold. As
applications, inequalities are proved for submanifolds with mutually orthogonal
distributions that include scalar and mutual curvature. For compact
submanifolds, inequalities are obtained that are supported by known integral
formulas for almost-product manifolds.
