Related papers: K-contact manifolds with minimal closed Reeb orbit…

LVM and LVMB manifolds are a large family of examples of non k\"ahler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a very natural action of the real torus and the…

In the breakthrough paper [V. Mu\~noz, A Smale-Barden manifold admitting K-contact but not Sasakian structure, 2024, 10.4171/JEMS/1496], it is constructed the first example of a simply connected compact 5-manifold (aka.\ Smale-Barden…

We show, as our main theorem, that if a Lipschitz map from a compact Riemannian manifold $M$ to a connected compact Riemannian manifold $N$, where $\dim M \geq \dim N$, has no singular points on $M$ in the sense of F.H. Clarke, then the map…

We study compatible contact structures of fibered Seifert multilinks in homology 3-spheres and especially give a necessary and sufficient condition for the contact structure to be tight in the case where the Seifert fibration is positively…

LVM and LVMB manifolds are a large family of examples of non kahler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a very natural action of the real torus and the…

It is known that any contact 3-manifold can be obtained by rational contact Dehn surgery along a Legendrian link L in the standard tight contact 3-sphere. We define and study various versions of contact surgery numbers, the minimal number…

In this article, we investigate Reeb dynamics on $b^m$-contact manifolds, previously introduced in [MiO], which are contact away from a hypersurface $Z$ but satisfy certain transversality conditions on $Z$. The study of these contact…

We introduce the classes of holomorphic $p$-contact manifolds and holomorphic $s$-symplectic manifolds that generalise the classical holomorphic contact and holomorphic symplectic structures. After observing their basic properties and…

Consider a symplectic surface in a three-dimensional contact manifold with boundary on Reeb orbits (periodic orbits of the Reeb vector field). We assume that the rotation numbers of the boundary Reeb orbits satisfy a certain inequality, and…

We introduce the notion of asymptotically finitely generated contact structures, which states essentially that the Symplectic Homology in a certain degree of any filling of such contact manifolds is uniformly generated by only finitely many…

Many authors have studied Ricci solitons and their analogs within the framework of (almost) contact geometry. In this article, we thoroughly study the $(m,\rho)$-quasi-Einstein structure on a contact metric manifold. First, we prove that if…

We present new explicit tight and overtwisted contact structures on the (round) 3-sphere and the (flat) 3-torus for which the ambient metric is weakly compatible. Our proofs are based on the construction of nonvanishing curl eigenfields…

Two constructions of contact manifolds are presented: (i) products of S^1 with manifolds admitting a suitable decomposition into two exact symplectic pieces and (ii) fibre connected sums along isotropic circles. Baykur has found a…

Contact round surgery of contact 3-manifolds is introduced in this paper. By using this method, an alternative proof of the existence of a contact structure on any closed orientable 3-manifold is given. It is also proved that any contact…

We construct, for any given positive integer $n$, Reeb flows on contact integral homology 3-spheres which do not admit global surfaces of section with fewer than $n$ boundary components. We use a connected sum operation for open books to…

We find a family of five dimensional completely solvable compact manifolds that constitute the first examples of $K$-contact manifolds which satisfy the Hard Lefschetz Theorem and have a model of Tievsky type just as Sasakian manifolds but…

We use contact fiber sums of open book decompositions to define an infinite hierarchy of filling obstructions for contact 3-manifolds, called planar k-torsion for nonnegative integers k, all of which cause the contact invariant in Embedded…

A class of examples of Riemannian metrics with holonomy G_2 on compact 7-manifolds was constructed by the author in arXiv:math.DG/0012189 and later in a joint work with N.-H. Lee in arXiv:0810.0957, using a certain `generalized connected…

We study low-dimensional problems in topology and geometry via a study of contact and Cauchy-Riemann ($CR$) structures. A contact structure is called spherical if it admits a compatible spherical $CR$ structure. We will talk about spherical…

We determine the homotopy type of isotropic torus complements in closed contact manifolds in terms of Reeb dynamics of special contact forms. For that we utilize holomorphic curve techniques known from symplectic field theory as…