Abstract:
We study deformation of spherical $CR$ circle bundles over Riemann surfaces of genus > 1. There is a one to one correspondence between such deformation space and the so-called universal Picard variety. Our differential-geometric proof of the structure and dimension of the unramified universal Picard variety has its own interest, and our theory has its counterpart in the Teichmuller theory.

Abstract:
We construct a versal family of deformations of CR structures in five dimensions, using a differential complex closely related to the differential form complex introduced by Rumin for contact manifolds.

Abstract:
Using the correction terms in Heegaard Floer theory, we find infinite examples of hyperbolic 3-manifolds that admit no weakly symplectically fillable contact structures.

Abstract:
The present study analyzed new and recast Ni-Cr alloys, regarding the relationship between the applied force and the deformation in cantilevered bar segments, with dimensions of 4.0 mm, 3.5 mm, 3.0 mm in thickness, 4.5 mm width and 15 mm length, on a universal testing machine “EMIC”. The bars in the tests were initially obtained acrylic resin by 4.8 mm wide × 4.3 mm thick × 4 cm long. We obtained 30 bars divided into two groups, with 15 to test new alloys and 15 with alloys recast. The alloy used was Tilite. For the application of the load, the bars were attached to “EMIC” where the active tip of 200 kgf load cell was at a specific point of the bar (15 mm) with a speed of 0.5 mm per minute. The data showed statistically significant differences in relation to alloys and thickness among the bars, and all thicknesses evaluated were different. Thus, it was concluded that there was statistically significant difference between the groups and their variables, and that the alloys recast could be reused at least 1 time, without loss of properties.

Abstract:
In this short note, we exhibit an infinite family of hyperbolic rational homology $3$--spheres which do not admit any fillable contact structures. We also note that most of these manifolds do admit tight contact structures.

Abstract:
A geometric obstruction, the so called "plastikstufe", for a contact structure to not being fillable has been found by K. Niederkruger. This generalizes somehow the concept of overtwisted structure to dimensions higher than 3. This paper elaborates on the theory showing a big number of closed contact manifolds with a "plastikstufe". They are the first examples of non-fillable contact closed high-dimensional manifolds. In particular we show that $S^3 \times \prod_j \Sigma_{j}$, for $g(\Sigma_j)\geq 2$, possesses this kind of contact structure and so any connected sum with those manifolds also does it.

Abstract:
We study the fillability (or embeddability) of 3-dimensional $CR$ structures under the geometric flows. Suppose we can solve a certain second order equation for the geometric quantity associated to the flow. Then we prove that if the initial $CR$ structure is fillable, then it keeps having the same property as long as the flow has a solution. We discuss the situation for the torsion flow and the Cartan flow. In the second part, we show that the above mentioned second order operator is used to express a tangency condition for the space of all fillable or embeddable $CR$ structures at one embedded in $\mathbb{C}^{2}.$

Abstract:
We show that the canonical contact structure on the link of a normal complex singularity is universally tight. As a corollary we show the existence of closed, oriented, atoroidal 3-manifolds with infinite fundamental groups which carry universally tight contact structures that are not deformations of taut (or Reebless) foliations. This answers two questions of Etnyre.

Abstract:
We study the existence of positive loops of contactomorphisms on a Liouville-fillable contact manifold $(\Sigma,\xi=\ker(\alpha))$. Previous results show that a large class of Liouville-fillable contact manifolds admit contractible positive loops. In contrast, we show that for any Liouville-fillable $(\Sigma,\alpha)$ with $\dim(\Sigma) \geq 7$, there exists a Liouville-fillable contact structure $\xi'$ on $\Sigma$ which admits no positive loop at all. Further, $\xi'$ can be chosen to agree with $\xi$ on the complement of a Darboux ball.