Contact manifold

Summary

A contact manifold is an odd-dimensional smooth manifold with a field of hyperplanes. This field is as far as possible from being tangent to a family of hypersurfaces. Contact geometry is the odd-dimensional sister of symplectic geometry. Level sets of energy in phase space, unit cotangent bundles and spaces of first-order jets carry natural contact structures. It is the setting of geometric optics, thermodynamics and Legendrian knot theory.