contact geometry

Noun

 * 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 study of such structures.
 * 2) * 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,
 * A contact manifold $$(M,\zeta)$$ is a $$(2n+1)$$-dimensional manifold $$M$$ equipped with a smooth maximally nonintegrable hyperplane field $$\zeta\subset{TM}$$, i.e., locally, $$\zeta=\ker\alpha$$, where $$\alpha$$ is a 1-form which satisfies $$\alpha\wedge(d\alpha)^n\ne 0$$. Since $$d\alpha$$ is a nondegenerate 2-form when restricted to $$\zeta$$, contact geometry is customarily viewed as the odd-dimensional sibling of symplectic geometry. Although contact geometry in dimensions $$\ge$$ 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.
 * 1) * 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 a sphere-sphere contact geometry.
 * 1) * 2003, Kurt Frischmuth, Dirk, Langemann, Distributed Numerical Calculations of Wear in the Rail-Wheel Contact, Karl Popp, Werner Schliehlen (editors), System Dynamics and Long-Term Behaviour of Railway Vehicles, Track and Subgrade, Springer, page 94,
 * Along the trajectories dissipated power is calculated and projected onto the surface grid by a method using geometrical data on the contact geometry.
 * Surfaces of even the large hydrate particles have rounded protrusions and are best represented by a sphere-sphere contact geometry.
 * 1) * 2003, Kurt Frischmuth, Dirk, Langemann, Distributed Numerical Calculations of Wear in the Rail-Wheel Contact, Karl Popp, Werner Schliehlen (editors), System Dynamics and Long-Term Behaviour of Railway Vehicles, Track and Subgrade, Springer, page 94,
 * Along the trajectories dissipated power is calculated and projected onto the surface grid by a method using geometrical data on the contact geometry.

Translations

 * German: Kontaktgeometrie