Editing Contact geometry (section)

===Properties===
It follows from the [[Frobenius theorem (differential topology)|Frobenius theorem on integrability]] that the contact field ''ξ'' is ''completely nonintegrable''. This property of the contact field is roughly the opposite of being a field formed from the tangent planes of a family of nonoverlapping hypersurfaces in ''M''. In particular, you cannot find a hypersurface in ''M'' whose tangent spaces agree with ''ξ'', even locally. In fact, there is no submanifold of dimension greater than ''k'' whose tangent spaces lie in ''ξ''.