contact geometry

noun2

1. •
   Given a smooth manifold of odd dimensionality, a distribution (subset) of the tangent bundle that satisfies the condition of complete nonintegrability, or equivalently may be locally defined as the kernel of a maximally nondegenerate differential 1-form;

   • The defining conditions for a contact geometry are opposite to two equivalent conditions for complete integrability of a hyperplane distribution: i.e. that it be tangent to a codimension 1 foliation on the manifold, whose equivalence is the content of the Frobenius theorem.
   • The contact geometry is in many ways an odd-dimensional counterpart of the symplectic geometry, a structure on certain even-dimensional manifolds. The concepts of contact geometry and symplectic geometry are both motivated by the mathematical formalism of classical mechanics, where one can consider either the even-dimensional phase space of a mechanical system or the constant-energy hypersurface, which, being of codimension 1, has odd dimension.
2. •
   the study of such structures.