contact geometry
Word Rarity
Rare
Frequency: Zipf frequency 3.85 in modern English
25
Scrabble Score
15
Letters
7
Syllables
10
Unique Chars
Meaning
noun
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;
Countable
noun
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.
Uncountable
Example Sentences
- "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."
- "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,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."
- "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."
- "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."