contact geometries

Noun

contact geometry (countable and uncountable, plural contact geometries)

1. (countable, differential geometry) 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.
2. (uncountable, differential geometry) the study of such structures.
3. Used other than figuratively or idiomatically: see contact, geometry.
   • 1998 [Kluwer Academic], L.-S. Fan, et al., Chapter 4: Sorbent Transfer and Dispersion, Barbara Toole-O'Neil (editor), Dry Scrubbing Technologies for Flue Gas Desulfurization, 1998, Springer, page 263,
     Surfaces of even the large hydrate particles have rounded protrusions and are best represented by...