5 papers
Bott-integrable contact forms with large systolic ratio
Hansjörg Geiges, Jakob Hedicke, Murat Sağlam
We show that there is no universal upper bound for the systolic ratio of Bott-integrable contact forms on closed 3-manifolds, thus providing further evidence for the relative flexi…
On contact mapping classes of prequantizations
Souheib Allout, Murat Sağlam
We present examples of prequantizations over integral symplectic manifolds which admit infinitely many smoothly trivial contact mapping classes. These classes are given by the conn…
Holomorphic curves in the symplectizations of lens spaces: an elementary approach
Murat Sağlam
We present an elementary computational scheme for the moduli spaces of rational pseudo-holomorphic curves in the symplectizations of 3-dimensional lens spaces, which are equipped w…
Reeb flows with small contact volume and large return time to a global section
Murat Sağlam
We show that any co-oriented closed contact manifold of dimension at least five admits a contact form such that the contact volume is arbitrarily small but the Reeb flow admits a g…
Contact forms with large systolic ratio in arbitrary dimensions
Murat Sağlam
If a contact form on a (2n+1)-dimensional closed contact manifold admits closed Reeb orbits, then its systolic ration is defined to be the quotient of (n+1)th power of the shortest…