相关论文: Normal CR structures on compact 3-manifolds

We study regular contact manifolds $(M,\eta)$ whose Reeb vector field is complete and prove that they are canonically principal bundles with the structure group $S^1$ or $\mathbb{R}$. For compact $M$, our proof is very short and elementary…

We continue the program of Chinea, De Leon and Marrero who studied the topology of cosymplectic manifolds. We study 3-cosymplectic manifolds which are the closest odd-dimensional analogue of hyper-Kaehler structures. We show that there is…

Let M be a connected generic real-analytic CR-submanifold of a finite-dimensional complex vector space E. Suppose that for every point a in M the Lie algebra hol(M,a) of germs of all infinitesimal real-analytic CR-automorphisms of M at a is…

Real-analytic CR functions on real-analytic CR singular submanifolds are not in general restrictions of holomorphic functions, unlike in the CR nonsingular case. We give a simple condition that completely characterizes those quadric CR…

In this paper, we generalize the CR Obata theorem to a compact strictly pseudoconvex CR manifold with a weighted volume measure. More precisely, we first derive the weighted CR Reilly's formula associated with the Witten sub-Laplacian and…

It is well known that a unit sphere admits Sasakian 3-structure. Also, Sasakian manifolds are locally isometric to a unit sphere under several curvature and critical conditions. So, a natural question is: Does there exist any curvature or…

Motivated by possible applications to meromorphic dynamics, and generalising known properties of difference-closed fields, this paper studies the theory CCMA of compact complex manifolds with a generic automorphism. It is shown that while…

Compact Vaisman manifolds with vanishing first Chern class split into three categories, depending on the sign of the Bott-Chern class. We show that Vaisman manifolds with non-positive Bott-Chern class admit canonical metrics, are…

We study the isometry groups of compact spherical orientable $3$-orbifolds $S^3/G$, where $G$ is a finite subgroup of $\mathrm{SO}(4)$, by determining their isomorphism type. Moreover, we prove that the inclusion of $\mbox{Isom}(S^3/G)$…

In this paper we prove weak L^{1,p} (and thus C^{\alpha}) compactness for the class of uniformly mean-convex Riemannian n-manifolds with boundary satisfying bounds on curvature quantities, diameter, and (n-1)-volume of the boundary. We…

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 refine the affine classification of real nets of quadrics in order to obtain generic curvature loci of regular $3$-manifolds in $\mathbb{R}^6$ and singular corank $1$ $3$-manifolds in $\mathbb{R}^5$. For this, we characterize the type of…

We investigate harmonic unit vector fields with totally geodesic integral curves on 3-manifolds. Under mild curvature assumptions, we classify both the vector fields and the manifolds that support them. Our results are inspired by…

Almost paracontact metric manifolds are the famous examples of almost para-CR manifolds. We find necessary and suffcient conditions for such manifolds to be para-CR. Next we examine these conditions in certain subclasses of almost…

We determine the curvature equations of natural metrics on tangent bundles and radius r tangent sphere bundles S_rM of a Riemannian manifold M. A family of positive scalar curvature metrics on S_rM is found, for any M with bounded sectional…

Locally homogeneous CR-manifolds in dimension 3 were classified, up to local CR-equivalence, by E.Cartan. We classify, up to local CR-equivalence, all locally homogeneous CR-manifolds in dimension 4. The classification theorem enables us…

We study the Sasaki cone of a CR structure of Sasaki type on a given closed manifold. We introduce an energy functional over the cone, and use its critical points to single out the strongly extremal Reeb vectors fields. Should one such…

Using the Sasakian join construction with homology 3-spheres, we give a countably infinite number of examples of Sasakian manifolds with perfect fundamental group in all odd dimensions greater than 1. These have extremal Sasaki metrics with…

We define the class of high dimensional graph manifolds. These are compact smooth manifolds supporting a decomposition into finitely many pieces, each of which is diffeomorphic to the product of a torus with a finite volume hyperbolic…

We apply the theory of finite-type invariants of homology 3-spheres to investigate the structure of the Torelli group. We construct natural cocycles in the Torelli group and show that the lower central series quotients of the Torelli group…