 Geometrically, this contact structure can be regarded as the distribution of (2"n"−2)-planes which, at the unit vector "u", is the pullback of the orthogonal complement of "u" in the tangent space of "M".This is a contact structure, for the fiber of UT"M" is obviously an integral manifold (the vertical bundle is everywhere in the kernel of θ), and the remaining tangent directions are filled out by moving up the fiber of UT"M".Thus the maximal integral manifold of θ is (an open set of) "M" itself.