Noun
(differential geometry, countable) 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;(uncountable) the study of such structures.
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.
Used other than figuratively or idiomatically: see contact, geometry.
Source: en.wiktionary.orgThis is false in dimensions greater than 3. Contact geometry main Contact geometry deals with certain manifolds of odd dimension. Source: Internet