Contact type

In mathematics, more precisely in symplectic geometry, a hypersurface $\Sigma$ of a symplectic manifold $(M,\omega )$ 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, where $j:\Sigma \to M$ is the natural inclusion.^[1] The terminology was first coined by Alan Weinstein.

References

Blair, David E. (2010). Riemannian geometry of contact and symplectic manifolds. Progress in Mathematics. Vol. 203 (Second edition of 2002 original ed.). Boston, MA: Birkhäuser Boston, Ltd. doi:10.1007/978-0-8176-4959-3. ISBN 978-0-8176-4958-6. MR 2682326. Zbl 1246.53001.
McDuff, Dusa; Salamon, Dietmar (2017). Introduction to symplectic topology. Oxford Graduate Texts in Mathematics (Third edition of 1995 original ed.). Oxford: Oxford University Press. doi:10.1093/oso/9780198794899.001.0001. ISBN 978-0-19-879490-5. MR 3674984. Zbl 1380.53003.