Related papers: Real analytic curves of almost complex structures

Let (X,I,J,K) be a compact hypercomplex manifold, i.e. a smooth manifold X with an action of the quaternion algebra (Id,I,J,K) on the tangent bundle TX, inducing integrable almost complex structures. For any $(a, b, c) \in S^2$, the linear…

We describe two constructions of (very) dense graphs which are edge disjoint unions of large {\em induced} matchings. The first construction exhibits graphs on $N$ vertices with ${N \choose 2}-o(N^2)$ edges, which can be decomposed into…

We study the existence of almost complex structures on even-dimensional sphere bundles over complex projective spaces. For bundles $\xi_{n,q}$ with fibre $S^{2q}$ over $\mathbb{C} P^n$, we establish a necessary condition: if $q \ge a(n)$…

A Nijenhuis operator on a manifold $M$ is a $(1,1)$ tensor $\mathcal N$ whose Nijenhuis-torsion vanishes. A Nijenhuis operator $\mathcal N$ on $M$ determines a Lie algebroid structure $(TM)_{\mathcal N}$ on the tangent bundle $TM$. In this…

We investigate T-duality transformation on an almost bi-hermitian space with torsion. By virtue of the Buscher rule, we completely describe not only the covariant derivative of geometrical objects but also the Nijenhuis tensor. We apply…

We built the pluripotential theory on almost complex surfaces. Using Bedford-Taylor type relative capacities we prove among others that J-holomorphic curves as well as negligible sets are pluripolar and Josefson's type theorem on almost…

Let X be e quasi-compact and semi-separated scheme. If every at quasi- coherent sheaf has finite cotorsion dimension, we prove that X is n-perfect for some n > 0. If X is coherent and n-perfect(not necessarily of finite krull dimension), we…

We investigate C-sets in almost zero-dimensional spaces, showing that closed $\sigma$C-sets are C-sets. As corollaries, we prove that every rim-$\sigma$-compact almost zero-dimensional space is zero-dimensional and that each cohesive almost…

In this article, we discuss the spaces of harmonic forms $\mathcal{H}^{\bullet}_{d}$ over a closed almost K\"{a}hler manifold $(X, J,\omega)$. We show that if the almost complex structure $J$ on the almost K\"{a}hler manifold $X$ is not too…

We find new examples of complex surfaces with countably many non-isomorphic algebraic structures. Here is one such example: take an elliptic curve $E$ in $\mathbb P^2$ and blow up nine general points on $E$. Then the complement $M$ of the…

If E is a nonempty closed subset of the locally finite Hausdorff (2n-2)-measure on an n-dimensional complex manifold M and all points of E are nonremovable for a meromorphic mapping of M \ E into a compact K\"ahler manifold, then E is a…

This article investigates the subject of rigid compact complex manifolds. First of all we investigate the different notions of rigidity (local rigidity, global rigidity, infinitesimal rigidity, etale rigidity and strong rigidity) and the…

We study tensors on Lie groupoids suitably compatible with the groupoid structure, called {\em multiplicative}. Our main result gives a complete description of these objects only in terms of infinitesimal data. Special cases include the…

An {\em almost p-K\"ahler manifold} is a triple $(M,J,\Omega)$, where $(M,J)$ is an almost complex manifold of real dimension $2n$ and $\Omega$ is a closed real tranverse $(p,p)$-form on $(M,J)$, where $1\leq p\leq n$. When $J$ is…

For k at least 2, we exhibit complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not locally affine homogeneous (and hence not locally homogeneous). The curvature tensor of these manifolds is modeled on…

We introduce a notion of compatibility between (almost) Dirac structures and (1,1)-tensor fields extending that of Poisson-Nijenhuis structures. We study several properties of the "Dirac-Nijenhuis" structures thus obtained, including their…

For the standard metric on the six-dimensional sphere, with Levi-Civita connection $\nabla$, we show there is no almost complex structure $J$ such that $\nabla_X J$ and $\nabla_{JX} J$ commute for every $X$, nor is there any integrable $J$…

We study the real analyticity of a CR mapping on the hypersurface $\h$ defined by $\h=\{z\in\C^n,\Re(z_n)+|z'|^2=0\}$ in model almost complex manifolds. We make use of a method of prolongation for the tangential Cauchy-Riemann equations and…

We classify the nilpotent Lie algebras of real dimension eight and minimal center that admit a complex structure. Furthermore, for every such nilpotent Lie algebra $\mathfrak{g}$, we describe the space of complex structures on…

We give a proof of the Gromov compactness theorem using the language of stable curves (i.e. cusp-curve of Gromov, or stable maps of Kontsevich and Manin) in general setting: An almost complex structure on a target manifold is only…