相关论文: On contact p-spheres

This paper is about the integrability of complex vector fields in dimension three in a neighborhood of a singular point. More precisely, we study the existence of holomorphic first integrals for isolated singularities of holomorphic vector…

This paper deals with the generalization of usual round spheres in the flat Minkowski spacetime to the case of a generic four-dimensional spacetime manifold $M$. We consider geometric properties of sphere-like submanifolds in $M$ and…

Let $\mathrm S^3$ be the unit sphere of $\mathbb C^2$ with its standard Cauchy-Riemann (CR) structure. This paper investigates the CR geometry of curves in $\mathrm S^3$ which are transversal to the contact distribution, using the local CR…

We continue the study of linear families of contact forms on 3-manifolds begun in our paper `Contact geometry and complex surfaces'. The present paper introduces Teichmuller and moduli spaces for so-called taut contact circles. By…

For a closed connected manifold N, we establish the existence of geometric structures on various subgroups of the contactomorphism group of the standard contact jet space J^1N, as well as on the group of contactomorphisms of the standard…

We study a class of simply connected manifolds in all odd dimensions greater than 3 that exhibit an infinite number of toric contact structures of Reeb type that are inequivalent as contact structures. We compute the cohomology ring of our…

We consider a closed orientable Riemannian 3-manifold $(M,g)$ and a vector field $X$ with unit norm whose integral curves are geodesics of $g$. Any such vector field determines naturally a 2-plane bundle contained in the kernel of the…

For a compact connected manifold M of dimension n greater than 3 and with no metric of positive scalar curvature, we prove that the Yamabe invariant is unchanged under surgery on spheres of dimension different from 1, n-2 and n-1. We use…

We use the Boothby-Wang fibration to construct certain simply connected K-contact manifolds and we give sufficient and necessary conditions on when such K-contact manifolds are homeomorphic to the odd dimensional spheres. If the symplectic…

We consider each of the three classes of representations of cyclic groups that arise in the study of rational sphere maps. We study the possible number of terms for invariant polynomials with non-negative coefficients that are constant on…

The first goal of this paper is to construct examples of higher dimensional contact manifolds with specific properties. Our main results in this direction are the existence of tight virtually overtwisted closed contact manifolds in all…

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…

For contact manifolds in dimension three, the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent. We extend these facts to higher dimensions: in particular, we define a natural generalization of…

We obtain several results for (iterated) planar contact manifolds in higher dimensions: (1) Iterated planar contact manifolds are not weakly symplectically semi-fillable. This generalizes a 3-dimensional result of Etnyre to a…

We exhibit the first examples of contact structures on $S^{2n-1}$ with $n\geq 4$ and on $S^3\times S^2$, all equipped with their standard smooth structures, for which every Reeb flow has positive topological entropy. As a new technical tool…

The goal of this article is to establish estimates involving the Yamabe minimal volume, mixed minimal volume and some topological invariants on compact 4-manifolds. In addition, we provide topological sphere theorems for compact…

We investigate the effect of a hyperbolic (or, more generally, isolated as an invariant set) closed Reeb orbit on the dynamics of a Reeb flow on the $(2n-1)$-dimensional standard contact sphere, extending two results previously known for…

Plastikstufes and overtwistedness for higher-dimensional contact manifolds are studied in this paper. It is proved that a contact structure is overtwisted if and only if there exists a small plastikstufe with toric core that has trivial…

We study hyper-spheres, spheres and circles, with respect to an indefinite metric, in a tangent space on a 4-dimensional differentiable manifold. The manifold is equipped with a positive definite metric and an additional tensor structure of…

In the spirit of Sullivan's paper "Cycles for the Dynamical Study of Foliated Manifolds and Complex Manifolds", existence of a contact structure on a closed manifold $M$ is shown to be equivalent to existence of an ample $S^1$-invariant…