Related papers: Pseudo-Einstein structure, eigenvalue estimate for…

The Newman-Penrose-Perjes formalism is applied to Sasakian 3-manifolds and the local form of the metric and contact structure is presented. The local moduli space can be parameterised by a single function of two variables and it is shown…

In this paper, we show that there exists a nonconstant CR holomorphic function of polynomial growth in a complete noncompact Sasakian manifold of nonnegative pseudohermitian bisectional curvature with the CR maximal volume growth property.…

We re-visit the eigenvalue estimate of the Dirac operator on spin manifolds with boundary in terms of the first eigenvalues of conformal Laplace operator as well as the conformal mean curvature operator. These problems were studied earlier…

Let $M$ be a pseudoconvex, oriented, bounded and closed CR submanifold of $\mathbb{C}^{n}$ of hypersurface type. Our main result says that when a certain $1$-form on $M$ is exact on the null space of the Levi form, then the complex Green…

A version of Lichnerowicz' theorem giving a lower bound of the eigenvalues of the sub-Laplacian under a lower bound on the Sp(1)Sp(1) component of the qc-Ricci curvature on a compact seven dimensional quaternionic contact manifold is…

Let X be a complex manifold with strongly pseudoconvex boundary M. If u is a defining function for M, then -log u is plurisubharmonic on a neighborhood of M in X, and the (real) 2-form s = i \del \delbar(-log u) is a symplectic structure on…

The purpose of this note is to introduce a new method for proving the existence of Sasakian-Einstein metrics on certain simply connected odd dimensional manifolds. We then apply this method to prove the existence of new Sasakian-Einstein…

The purpose of this article is to study compactness of the complex Green operator on CR manifolds of hypersurface type. We introduce (CR-P_q), a potential theoretic condition on $(0,q)$-forms that generalizes Catlin's property (P_q) to CR…

The main purpose of this work is to generalize the $S^3_\bfw$ Sasaki join construction $M\star_\bfl S^3_\bfw$ described in \cite{BoTo14a} when the Sasakian structure on $M$ is regular, to the general case where the Sasakian structure is…

This paper provides a connection between two distinct branches of research in CR geometry -- namely, analytic and geometric conditions that suffice to establish the closed range of the Cauchy-Riemann operator and CR invariants on CR…

We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem by using intersection…

In the study of the extremal for Sobolev inequality on the Heisenberg group and the Cauchy-Riemann(CR) Yamabe problem, Jerison-Lee found a three-dimensional family of differential identities for critical exponent subelliptic equation on…

We obtain a Bochner type formula and an estimate from below on the spectrum of the sublaplacian of a compact strictly pseudoconvex CR manifold.

A compact Riemannian manifold is associated with geometric data given by the eigenvalues of various Laplacian operators on the manifold and the triple overlap integrals of the corresponding eigenmodes. This geometric data must satisfy…

We introduce the concept of $\varepsilon\,$-contact metric structures on oriented (pseudo-)Riemannian three-manifolds, which encompasses the usual Riemannian contact metric, Lorentzian contact metric and para-contact metric structures, but…

The metrics of S. Y. Cheng and S.-T. Yau are considered on a strictly pseudoconvex domains in a complex manifold. Such a manifold carries a complete K\"{a}hler-Einstein metric if and only if its canonical bundle is positive. We consider the…

Given two closed contact three-manifolds, one can form their contact connected sum via the Weinstein one-handle attachment. We study how pseudo-holomorphic curves in the symplectization behave under this operation. As a result, we give a…

The aim of the present papar is to study the orbits of the isotropy gourp action on an irreducible Hermitian symmetric space of compact type. Specifically, we examine the properties of these orbits as {\it CR} submanifolds of a K\"{a}hler…

The purpose of this paper is to introduce a geometric structure called pseudo-conformal quaternionic CR structure on a (4n+3)-dimensional mamnifold and then exhibit a quaternionic analogue of Chern-Moser's CR structure and uniformization.

The $Q$-prime curvature is a local pseudo-Einstein invariant on CR manifolds defined by Case and Yang, and Hirachi. Its integral, the total $Q$-prime curvature, gives a non-trivial global CR invariant. On the other hand, Marugame has…