Related papers: Real analytic curves of almost complex structures

We classify compact surfaces with torsion-free affine connections for which every geodesic is a simple closed curve. In the process, we obtain completely new proofs of all the major results concerning the Riemannian case. In contrast to…

Let $M_i$, for $i=1,2$, be a K\"ahler manifold, and let $G$ be a Lie group acting on $M_i$ by K\"ahler isometries. Suppose that the action admits a momentum map $\mu_i$ and let $N_i:=\mu_i^{-1}(0)$ be a regular level set. When the action of…

This paper forms the third part of a series by the authors [GMV1,GMV2] concerning the structure theory of nilspaces. A nilspace is a compact space $X$ together with closed collections of cubes $C^n(X)\subseteq X^{2^n}$, $n=1,2,\ldots$,…

We show that for all $n \ge 3$, any $(2n+1)$-dimensional manifold that admits a tight contact structure, also admits a tight but non-fillable contact structure, in the same almost contact class. For $n=2$, we obtain the same result,…

We prove that for any open orientable surface $S$ of finite topology, there exist a Riemann surface $\mathcal{M},$ a relatively compact domain $M\subset\mathcal{M}$ and a continuous map $X:\bar{M}\to\mathbb{C}^3$ such that: $\mathcal{M}$…

The main purpose of the paper is to establish a closedness theorem over Henselian valued fields $K$ of equicharacteristic zero (not necessarily algebraically closed) with separated analytic structure. It says that every projection with a…

In this paper we determine the Gray-Hervella classes of the compatible almost complex structures on the twistor spaces of oriented Riemannian four-manifolds considered by G. Deschamps

We study the J-invariant and J-anti-invariant cohomological subgroups of the de Rham cohomology of a compact manifold M endowed with an almost-K\"ahler structure (J, \omega, g). In particular, almost-K\"ahler manifolds satisfying a…

We complete our recent classification of compact inner symmetric spaces with weakly complex tangent bundle by filling up a case which was left open, and extend this classification to the larger category of compact homogeneous spaces with…

This note is concerned in so called harmonic complex structures introduced by the author previously. I will recall some previous results and emphasize the motivation: Provide an attempt to a fundamental problem in geometry--determining the…

An almost complex structure J on a 4-manifold X may be described in terms of a rank 2 vector bundle E. A splitting of J consists of a pair of line bundles spanning E. A hypersurface M in X satisfying a nondegeneracy condition inherits a…

Nijenhuis tensors $N$ on Courant algebroids compatible with the pairing are studied. This compatibility condition turns out to be of the form $N+N^*=aI$ for irreducible Courant algebroids, in particular for the extended tangent bundles…

For each compact almost Kahler manifold $(X,\om,J)$ and an element A of $H_2(X;Z)$, we describe a closed subspace $\ov{\frak M}_{1,k}^0(X,A;J)$ of the moduli space $\ov{\frak M}_{1,k}(X,A;J)$ of stable J-holomorphic genus-one maps such that…

Given an idempotent complete additive category, we show the there is an explicitly constructed topological space such that the lattice of exact substructures is anti-isomorphic to the lattice of closed subsets. In the special case that the…

On negatively curved compact manifolds, it is possible to associate to every closed form a bounded cocycle - hence a bounded cohomology class - via integration over straight simplices. The kernel of this map is contained in the space of…

A Kaehler-Nijenhuis manifold is a Kaehler manifold M, with metric g, complex structure J and Kaehler form F, endowed with a Nijenhuis tensor field A that is compatible with the Poisson stucture defined by F in the sense of the theory of…

Geometric structures underlying commutative and non commutative integrable dynamics are analyzed. They lead to a new characterization of noncommutative integrability in terms of spectral properties and of Nijenhuis torsion of an invariant…

Let $(M,I,J,K)$ be a hyperkahler manifold, and $Z\subset (M,I)$ a complex subvariety in $(M,I)$. We say that $Z$ is trianalytic if it is complex analytic with respect to $J$ and $K$, and absolutely trianalytic if it is trianalytic with…

It is proved that if an almost K\"ahler manifold of dimension greater or equal to 8 is of pointwise constant antiholomorphic sectional curvature, then it is a complex space form.

In this paper we study Almost-Riemannian Structures (ARS) on the class of nonnilpotent, solvable, conneted 3D Lie groups. The nice structures present in such groups allow us to show that the singular locus of ARSs on such groups are always…