In mathematics, more precisely in

symplectic geometry Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the ...

, a

hypersurface In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic variety of dimension , which is embedded in an ambient space of dimension , generally a Eucl ...

\Sigma

of a

symplectic manifold In differential geometry, a subject of mathematics, a symplectic manifold is a smooth manifold, M , equipped with a closed nondegenerate differential 2-form \omega , called the symplectic form. The study of symplectic manifolds is called s ...

(M,\omega)

is said to be of contact type if there is 1-form

\alpha

such that

j^(\omega)=d\alpha

and

(\Sigma,\alpha)

is a

contact manifold In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete non-integrability'. Equivalently, such a distribution m ...

, where

j: \Sigma \to M

is the natural inclusion. The terminology was first coined by

Alan Weinstein Alan David Weinstein (17 June, 1943, New York City) is a professor of mathematics at the University of California, Berkeley, working in the field of differential geometry, and especially in Poisson geometry. Education and career Weinstein o ...

References

* * Symplectic geometry {{differential-geometry-stub

See also

References