Contact type

In mathematics, more precisely in symplectic geometry, a hypersurface ${\displaystyle \Sigma }$ of a symplectic manifold ${\displaystyle (M,\omega )}$ is said to be of contact type if there is 1-form ${\displaystyle \alpha }$ such that ${\displaystyle j^{*}(\omega )=d\alpha }$ and ${\displaystyle (\Sigma ,\alpha )}$ is a contact manifold, where ${\displaystyle j:\Sigma \to M}$ is the natural inclusion. The terminology was coined by Alan Weinstein.

See also

• Weinstein conjecture

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.

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