Contact type

Short description: Symplectic manifold hypersurface

In mathematics, more precisely in symplectic geometry, a hypersurface [math]\displaystyle{ \Sigma }[/math] of a symplectic manifold [math]\displaystyle{ (M,\omega) }[/math] is said to be of contact type if there is 1-form [math]\displaystyle{ \alpha }[/math] such that [math]\displaystyle{ j^{*}(\omega)=d\alpha }[/math] and [math]\displaystyle{ (\Sigma,\alpha) }[/math] is a contact manifold, where [math]\displaystyle{ j: \Sigma \to M }[/math] is the natural inclusion.({{{1}}}, {{{2}}}) The terminology was first coined by Alan Weinstein.

See also

• Weinstein conjecture

References

• Blair, David E. (2010). Riemannian geometry of contact and symplectic manifolds. Progress in Mathematics. 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. 
• 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.