Related papers: Contact structures, CR Yamabe invariant, and conne…
We define an invariant of contact 3-manifolds with convex boundary using Kronheimer and Mrowka's sutured monopole Floer homology theory (SHM). Our invariant can be viewed as a generalization of Kronheimer and Mrowka's contact invariant for…
A pseudo-Einstein contact form plays a crucial role in defining some global invariants of closed strictly pseudoconvex CR manifolds. In this paper, we prove that the existence of a pseudo-Einstein contact form is preserved under…
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…
Consider a closed connected $3$-manifold $M$ acted diffeomorphically on by a compact Lie group $G$ with at least one orbit of finite cardinality. We show an upper bound for the $G$-equivariant Yamabe invariant $\sigma_G(M)$ under certain…
On a compact strictly pseudoconvex CR manifold $(M,\th)$, we consider the CR Yamabe constant of its infinite conformal covering. By using the maximum principles, we then prove a uniqueness theorem for the CR Yamabe flow on a complete…
An explicit classification of simply connected compact homogeneous CR manifolds G/L of codimension one, with non-degenerate Levi form, is given. There are three classes of such manifolds: a) the standard CR homogeneous manifolds which are…
A global secondary CR invariant is defined as the integral of a pseudo-hermitian invariant which is independent of a choice of pseudo-Einstein contact form. We prove that any global secondary CR invariant on CR five-manifolds is a linear…
This paper has two goals; the first is to generalize results for the existence and nonexistence of warped product submanifolds of almost contact manifolds, accordingly a self-contained reference of such submanifolds is offered to save…
We introduce higher order mean curvatures of screen almost conformal (SAC) half-lightlike submanifolds of indefinite contact manifolds, admitting a semi-symmetric non-metric connection, and use them to generalize some known results of [6].…
We continue our previous work studying critical exponent semilinear elliptic (and subelliptic) problems which generalize the classical Yamabe problem. In [3] the focus was on metric-measure spaces with an `almost smooth' structure, with…
We prove that the Yamabe invariant of any simply connected smooth manifold of dimension n greater than four is non-negative. Equivalently that the infimum of the L^{n/2} norm of the scalar curvature, over the space of all Riemannian metrics…
In this article we introduce and analyze in detail singular contact structures, with an emphasis on $b^m$-contact structures, which are tangent to a given smooth hypersurface $Z$ and satisfy certain transversality conditions. These singular…
A result from Gromov ensures the existence of a contact structure on any connected non-compact odd dimensional Lie group. But in general such structures are not invariant under left translations of the Lie group. The problem of finding…
We show that the S^1-equivariant Yamabe invariant of the 3-sphere, endowed with the Hopf action, is equal to the (non-equivariant) Yamabe invariant of the 3-sphere. More generally, we establish a topological upper bound for the…
The critical CR GJMS operator on a strictly pseudoconvex CR manifold is a non-hypoelliptic CR invariant differential operator. We prove that, under the embeddability assumption, it is essentially self-adjoint and has closed range. Moreover,…
We derive new existence results for tight contact structures on certain 3-manifolds which can be presented as surgery along specific knots in S^3. Indeed, we extend our earlier results on knots with maximal Thurston-Bennequin number being…
For a nullhomologous Legendrian knot in a closed contact 3-manifold Y we consider a contact structure obtained by positive rational contact surgery. We prove that in this situation the Heegaard Floer contact invariant of Y is mapped by a…
It is known that the folded sum of two contact mapping tori whose fibers are compact exact symplectic manifolds having a common convex boundary (called the ``fold'') admits a cooriented contact structure compatible with the obvious…
We interpret the property of having an infinitesimal symmetry as a variational property in certain geometric structures. This is achieved by establishing a one-to-one correspondence between a class of cone structures with an infinitesimal…
In the present paper, we study globally framed f-manifolds in the particular setting of indefinite S-manifolds for both spacelike and timelike cases. We prove that if $M = N^{\perp} \times_f N^T$ is a warped CR-submanifold such that…