Related papers: Contact Moishezon threefolds with second Betti num…

A contact projective structure is a contact path geometry the paths of which are among the geodesics of some affine connection. In the manner of T.Y. Thomas there is associated to each contact projective structure an ambient affine…

Let M be an irreducible compact hyperk\"ahler manifold of complex dimension six. Under an assumption on the Looijenga-Lunts-Verbitsky decomposition of the cohomology of M, we prove that the second Betti number of M is at most 23.

We generalise the notion of contact manifold by allowing the contact distribution to have codimension two. There are special features in dimension six. In particular, we show that the complex structure on a three-dimensional complex contact…

We compute the Betti numbers and describe the cohomology algebras of the ordered and unordered configuration spaces of three points in complex projective spaces, including the infinite dimensional case. We also compute these invariants for…

We prove that for a finite set of points $X$ in the projective $n$-space over any field, the Betti number $\beta_{n,n+1}$ of the coordinate ring of $X$ is non-zero if and only if $X$ lies on the union of two planes whose sum of dimension is…

We show that the connected sum of two copies of real projective 3-space does not admit a real projective structure. This is the first known example of a connected 3-manifold without a real projective structure.

In this paper we investigate Moishezon twistor spaces which have a structure of double covering over a very simple rational threefold. These spaces can be regarded as a direct generalization of the twistor spaces studied by Poon and…

We present a necessary condition for $(\ell-1)$-connected combinatorial $(2\ell +1)$-manifolds to be tight. As a corollary, we show that there is no tight combinatorial three-manifold with Betti number at most two other than the boundary of…

In this paper, we show that there is no phi-recurrent Sasakian manifold. Then we prove that the only flat 3-dimensional manifolds are phi-recurrent (k, m)-contact metric manifolds.

We calculate explicitly the Betti numbers of a class of barely G2 manifolds - that is, G2 manifolds that are realised as a product of a Calabi-Yau manifold and a circle, modulo an involution. The particular class which we consider are those…

We show that the virtual i-th Betti number of acompact locally symmetric space is either the i-th Betti number of the compact dual or else is infinite.

We describe here two simple polytopes that have different Betti numbers and whose moment-angle manifolds are diffeomorphic.

In a paper (math.DG/0403528) we obtained explicit examples of Moishezon twistor spaces of some compact self-dual four-manifolds admitting a non-trivial Killing field, and also determined their moduli space. In this note we investigate…

We show that the complex projective space is the only projective manifold compactifying $\mathbb{C}^n$ by a smooth connected hypersurface, provided $n$ is even. In the odd dimensional case we give some partial results. The case when $n…

Let V be a closed 3-manifold. In this paper we prove that the homotopy classes of plane fields on V that contain tight contact structures are in finite number and that, if V is atoroidal, the isotopy classes of tight contact structures are…

In recent papers math.DG/0701278 and arXiv:0705.0060, we gave explicit description of some new Moishezon twistor spaces. In this paper, developing the method in the papers much further, we explicitly give projective models of a number of…

We consider Lorentzian manifolds with parallel light-like vector field V. Being parallel and light-like, the orthogonal complement of V induces a codimension one foliation. Assuming compactness of the leaves and non-negative Ricci curvature…

It is known that any two triangulations of a compact 3-manifold are related by finite sequences of certain local transformations. We prove here an upper bound for the length of a shortest transformation sequence relating any two…

A point q in a contact manifold is called a translated point for a contactomorphism \phi, with respect to some fixed contact form, if \phi(q) and q belong to the same Reeb orbit and the contact form is preserved at q. In this article we…

The purpose of this article is to study co-dimension $2$ iso-contact embeddings of closed contact manifolds. We first show that a closed contact manifold $(M^{2n-1}, \xi_M)$ iso-contact embeds in a contact manifold $(N^{2n+1}, \xi_N),$…