Contact type
Encyclopedia
In mathematics
, more precisely in symplectic geometry, a hypersurface
of a symplectic manifold
is said to be of contact type if there is 1-form 
such that 
and 
is a contact manifold, where 
is the natural inclusion. The terminology was first coined by Alan Weinstein
.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, more precisely in symplectic geometry, a hypersurface
Hypersurface
In geometry, a hypersurface is a generalization of the concept of hyperplane. Suppose an enveloping manifold M has n dimensions; then any submanifold of M of n − 1 dimensions is a hypersurface...
of a symplectic manifoldSymplectic manifold
In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2-form, ω, called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology...
is said to be of contact type if there is 1-form such that and is a contact manifold, where is the natural inclusion. The terminology was first coined by Alan WeinsteinAlan Weinstein
Alan David Weinstein is a professor of mathematics at the University of California, Berkeley who works in symplectic geometry, Poisson Geometry and Mathematical Physics....
.