Geometric Inequalities for a Submanifold Equipped with Distributions

The article introduces invariants of a Riemannian manifold related to the mutual curvature several pairwise orthogonal subspaces tangent bundle. In case one-dimensional subspaces, this is equal half scalar subspace spanned by them, and in complementary mixed curvature. We compared our with Chen proved geometric inequalities intermediate mean squared for submanifold. This gives sufficient conditions absence minimal isometric immersions manifolds Euclidean space. As applications, were obtained sub-Riemannian equipped mutually distributions.