See contact geometry in All languages combined, or Wiktionary
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"text": "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.",
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"text": "2004, Ko Honda, 3-Dimensional Methods in Contact Geometry, Simon Donaldson, Yakov Eliashberg, Misha Gromov (editors), Different Faces of Geometry, Springer (Kluwer Academic), page 47,\nA contact manifold (M,ζ) is a (2n+1)-dimensional manifold M equipped with a smooth maximally nonintegrable hyperplane field ζ⊂TM, i.e., locally, ζ= ker α, where α is a 1-form which satisfies α∧(dα)ⁿ ne 0. Since dα is a nondegenerate 2-form when restricted to ζ, contact geometry is customarily viewed as the odd-dimensional sibling of symplectic geometry. Although contact geometry in dimensions > 5 is still in an incipient state, contact structures in dimension 3 are much better understood, largely due to the fact that symplectic geometry in two dimensions is just the study of area."
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"text": "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,\nSurfaces of even the large hydrate particles have rounded protrusions and are best represented by a sphere-sphere contact geometry."
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