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.{{sfnm|1a1=Blair|1y=2010|1p=29|2a1=McDuff|2a2=Salamon|2y=2017|2loc=Definition 3.5.32}} The terminology was first coined by Alan Weinstein.

References

{{cite book|last1=Blair|first1=David E.|title=Riemannian geometry of contact and symplectic manifolds|edition=Second edition of 2002 original|series=Progress in Mathematics|volume=203|publisher=Birkhäuser Boston, Ltd.|location=Boston, MA|year=2010|mr=2682326|isbn=978-0-8176-4958-6|doi=10.1007/978-0-8176-4959-3|zbl=1246.53001}}
{{cite book|last1=McDuff|first1=Dusa|last2=Salamon|first2=Dietmar|title=Introduction to symplectic topology|edition=Third edition of 1995 original|series=Oxford Graduate Texts in Mathematics|publisher=Oxford University Press|location=Oxford|year=2017|isbn=978-0-19-879490-5|mr=3674984|author-link1=Dusa McDuff|author-link2=Dietmar Salamon|zbl=1380.53003|doi=10.1093/oso/9780198794899.001.0001}}

Category:Symplectic geometry

contact type

See also

References