Related papers: Contact structures, CR Yamabe invariant, and conne…

We consider the CR Yamabe flow on a compact strictly pseudoconvex CR manifold $M$ of real dimension $2n+1$. We prove convergence of the CR Yamabe flow when $n=1$ or $M$ is spherical.

In contact geometry, a systolic inequality is a uniform upper bound on the shortest period of a closed Reeb orbit, in terms of the contact volume. We prove a general systolic inequality valid on Seifert bundles with non-zero Euler number…

Extending a result of He to the non-integrable case of K-contact manifolds, it is shown that transverse Hermitian scalar curvature may be interpreted as a moment map for the strict contactomorphism group. As a consequence, we may generalize…

In this article we consider integrable systems on manifolds endowed with singular symplectic structures of order one. These structures are symplectic away from an hypersurface where the symplectic volume goes either to infinity or to zero…

In this paper, we deal with a strongly pseudoconvex almost CR manifold with a CR contraction. We will prove that the stable manifold of the CR contaction is CR equivalent to the Heisenberg group model.

We complete the classification (started by Bray and the second author) of all closed 3-manifolds with Yamabe invariant greater than that of $\RP^3$, by showing that such manifolds are either $S^3$ or finite connected sums $# m(S^2 \times…

Let $X$ be a CR manifold with transversal, proper CR $G$-action. We show that $X/G$ is a complex space such that the quotient map is a CR map. Moreover the quotient is universal, i.e. every invariant CR map into a complex manifold…

In previous work (arXiv:2205.12067), we defined a notion of a generalized Sasakian structure in the context of generalized contact geometry, the odd dimensional analogue of generalized complex geometry introduced by Hitchin and Gualtieri.…

The CR $\delta$-invariant for CR-submanifolds was introduced in a recent article [B. Y. Chen, An optimal inequality for CR-warped products in complex space forms involving CR $\delta$-invariant, Internat. J. Math. 23} (2012), no. 3, 1250045…

In this note we define three invariants of contact structures in terms of open books supporting the contact structures. These invariants are the support genus (which is the minimal genus of a page of a supporting open book for the contact…

In this paper, we derive a partial result related to a question of Yau: "Does a simply-connected complete K\"ahler manifold M with negative sectional curvature admit a bounded non-constant holomorphic function?" Main Theorem. Let $M^{2n}$…

We consider plumbings of symplectic disk bundles over spheres admitting concave contact boundary, with the goal of understanding the geometric properties of the boundary contact structure in terms of the data of the plumbing. We focus on…

We introduce the notion of pseudohermitian k-curvature, which is a natural extension of the Webster scalar curvature, on an orientable manifold endowed with a strictly pseudoconvex pseudohermitian structure (referred here as a CR manifold)…

We construct group-invariant CR maps from the unit sphere in $\mathbb{C}^3$ and provide sharp bounds for the gap termination in this setting.

We establish a quantitative relationship between mixed de Rham classes and the geometric complexity of metric connections with totally skew torsion on product manifolds where both factors are compact oriented surfaces. For any…

An octonionic contact (OC) manifold is always spherical. We construct the OC Yamabe operator on an OC manifold and prove its transformation formula under conformal OC transformations. An OC manifold is scalar positive, negative or vanishing…

We construct an invariant of closed ${\rm spin}^c$ 4-manifolds using families of Seiberg-Witten equations. This invariant is formulated as a cohomology class on a certain abstract simplicial complex consisting of embedded surfaces of a…

The Willmore energy, alias bending energy or rigid string action, and its variation-the Willmore invariant-are important surface conformal invariants with applications ranging from cell membranes to the entanglement entropy in quantum…

In this paper, we show that the Ozsv\'ath-Szab\'o contact invariant $c^+(\xi)\in HF^+(-Y)$ of a contact 3-manifold $(Y,\xi)$ can be calculated combinatorially if $Y$ is the boundary of a certain type of plumbing $X$, and $\xi$ is induced by…

We prove a surgery formula for the smooth Yamabe invariant $\sigma(M)$ of a compact manifold $M$. Assume that $N$ is obtained from $M$ by surgery of codimension at least 3. We prove the existence of a positive number $\Lambda_n$, depending…