Related papers: Almost complex parallelizable manifolds: Kodaira d…

Let $\left( M,J,g\right) $ be a metallic pseudo-Riemannian manifold equipped with a metallic structure $J$ and a pseudo-Riemannian metric $g$. The paper deals with interactions of Codazzi couplings formed by conjugate connections and tensor…

A compact K\"ahler manifold $\left( M,\omega ,J\right) $ with $T$-symmetry admits a natural mixed polarization $\mathcal{P}_{\mathrm{mix}}$ whose real directions come from the $T$-action. In \cite{LW1}, we constructed a one-parameter family…

Let $X$ be a four-dimensional projective variety defined over the field of complex numbers with only terminal singularities. We prove that if the intersection number of the canonical divisor $K$ with every very general curve is positive…

We investigate the geometry of the Kodaira moduli space $M$ of sections of $\pi:Z\to {\mathbb P}^1$, the normal bundle of which is allowed to jump from ${\mathcal O}(1)^{n}$ to ${\mathcal O}(1)^{n-2m}\oplus {\mathcal O}(2)^{m}\oplus…

A generalization to the almost complex setting of a well-known result by S. Webster is given. Namely, we prove that if $\Gamma$ is a strongly pseudoconvex hypersurface in an almost complex manifold $(M, J)$, then the conormal bundle of…

In this paper we consider the existence and regularity of weakly polyharmonic almost complex structures on a compact almost Hermitian manifold $M^{2m}$. Such objects satisfy the elliptic system weakly $[J, \Delta^m J]=0$. We prove a very…

Kostant gave a model for the real geometric quantization associated to polarizations via the cohomology associated to the sheaf of flat sections of a pre-quantum line bundle. This model is well-adapted for real polarizations given by…

We define homological dimensions for S-algebras, the generalized rings that arise in algebraic topology. We compute the homological dimensions of a number of examples, and establish some basic properties. The most difficult computation is…

In this article, we construct the reduced genus-two Gromov-Witten invariants for certain almost K\"{a}hler manifold $(X, \omega, J)$ such that $J$ is integrable and satisfies some regularity conditions. In particular, the standard…

The present paper studies the structure of characteristic varieties of fundamental groups of graph manifolds. As a consequence, a simple proof of Papadima's question is provided on the characterization of algebraic links that have…

Almost paracontact almost paracomplex Riemannian manifolds of the lowest dimension 3 are considered. Such structures are constructed on a family of Lie groups and the obtained manifolds are studied. Curvature properties of these manifolds…

A four-parametric family of linear connections preserving the almost complex structure is defined on an almost complex manifold with Norden metric. Necessary and sufficient conditions for these connections to be natural are obtained. A…

An n-dimensional complex manifold M is said to be (holomorphically) dominable by $\CC^n$ if there is a map $F:\CC^n \ra M$ which is holomorphic such that the Jacobian determinant $\det(DF)$ is not identically zero. Such a map F is called a…

We consider complete nearly K\"ahler manifolds with the canonical Hermitian connection. We prove some metric properties of strict nearly K\"ahler manifolds and give a sufficient condition for the reducibility of the canonical Hermitian…

Let $(\acute{N},g,\nabla )$\ be a $2n$-dimensional quasi-statistical manifold that admits a pseudo-Riemannian metric $g$ (or $h)$ and a linear connection $\nabla $ with torsion. This paper aims to study an almost Hermitian structure $(g,L)$…

In this paper, firstly, for some $4n$-dimensional almost complex manifolds $M_{i}, ~1\le i \le \alpha$, we prove that $\left(\sharp_{i=1}^{\alpha} M_{i}\right) \sharp (\alpha{-}1) \mathbb{C} P^{2n}$ must admits an almost complex structure,…

We study the local Killing Lie algebra of meromorphic almost rigid geometric structures on complex manifolds. This leads to classification results for compact complex manifolds bearing holomorphic rigid geometric structures.

In the first part of this paper we study geometric formality for generalized flag manifolds, including full flag manifolds of exceptional Lie groups. In the second part we deal with the problem of the classification of invariant almost…

For a strongly pseudo-convex complex Finsler manifold M, a bundle U of adapted unitary frames is canonically defined. A non-linear Hermitian connection on U, invariant under local biholomorphic isometries, is given and it proved to be…

The object of investigations are almost contact B-metric structures on 3-dimensional Lie groups considered as smooth manifolds. There are established the existence and some geometric characteristics of these manifolds in all basic classes.…