 The metric on "M" induces a contact structure on UT"M".This is given in terms of a tautological one-form, defined at a point "u" of UT"M" (a unit tangent vector of "M") by
where formula_6 is the pushforward along π of the vector "v" ∈ T"u"UT"M".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".