Related papers: Invariant Generalized Complex Structures on Flag M…

We construct a family of canonical connections and surrounding basic theory for almost complex manifolds that are equipped with an affine connection. This framework provides a uniform approach to treating a range of geometries. In…

By a theorem of Kirchhoff if the six sphere admits an almost complex structure then the seven sphere is parallelizable, more crucial, he exhibited an explicit global frame constructed out of the given almost complex structure. This result…

We observed in our previous paper that all the complex structures on four-dimensional compact solvmanifolds, including tori, are left-invariant. In this paper we will give an example of a six-dimensional compact solvmanifold which admits a…

We study generalized complex cohomologies of generalized complex structures constructed from certain symplectic fibre bundles over complex manifolds. We apply our results in the case of left-invariant generalized complex structures on…

We study the question of integrability of a compatible almost complex structure on a compact symplectic 4-manifold, under various natural assumptions on the curvature of the associated almost Kahler metric.

We study existence of complex structures on semidirect products $\g \oplus_{\rho} \v$ where $\g$ is a real Lie algebra and $\rho$ is a representation of $\g$ on $\v$. Our first examples, the Euclidean algebra $\e(3)$ and the Poincar\'e…

We introduce integrable complex structures on twistor spaces fibered over complex manifolds. We then show, in particular, that the twistor spaces associated with generalized Kahler, SKT and strong HKT manifolds all naturally admit complex…

We will have a deep look at the set of all $G$-equivariant maps from the factor Lie group $G$ to the under the action manifold $M$, both from "computational" and "observability" viewpoint. We will also be looking for the existence of…

In this paper, we study invariant Poisson structures on homogeneous manifolds, which serve as a natural generalization of homogeneous symplectic manifolds previously explored in the literature. Our work begins by providing an algebraic…

We show that $U(k)$-invariant hypercomplex structures on (open subsets) of regular semisimple adjoint orbits in $\mathfrak{gl}(k,{\mathbb C})$ correspond to algebraic curves $C$ of genus $(k-1)^2$, equipped with a flat projection…

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…

Let $N\subset GL(n,R)$ be the group of upper triangular matrices with $1$s on the diagonal, equipped with the standard Carnot group structure. We show that quasiconformal homeomorphisms between open subsets of $N$, and more generally…

In this paper, we study deformations of complex structures on Lie algebras and its associated deformations of Dolbeault cohomology classes. A complete deformation of complex structures is constructed in a way similar to the Kuranishi…

The space ${\mathcal A}$ of almost complex structures on a closed manifold $M$ is studied. A natural parametrization of the space ${\mathcal A}$ is defined. It is shown, that ${\mathcal A}$ is a infinite dimensional complex weak…

We prove that the isomorphism problem is decidable for generalized Baumslag-Solitar (GBS) groups with one quasi-conjugacy class and full support gaps. In order to do so we introduce a family of invariants that fully characterize the…

Let $G$ be a non-compact classical semisimple Lie group and let $G/V$ be the adjoint orbit with respect to a fixed element in $G$. These manifolds can be equipped with an almost-K\"ahler structure and we provide explicit formulae for the…

Let X=G/P be a complex flag manifold and E->X be a G-homogeneous holomorphic vector bundle. Fix a U-invariant Kaehler metric on X with U in G maximal compact. We study the sheaf of nearly holomorphic sections and show that the space of…

We present the classification of real nilpotent quasi-filiform Lie algebras endowed with a complex structure. A nilpotent Lie algebra g is called quasi-filiform is the nilindex is equal to dim(n)-2. We recall that the filiform case…

We prove that the group of normalized cohomological invariants of degree 3 modulo the subgroup of semidecomposable invariants of a semisimple split linear algebraic group G is isomorphic to the torsion part of the Chow group of codimension…

In this article, we study compactifications of homogeneous spaces coming from equivariant, open embeddings into a generalized flag manifold $G/P$. The key to this approach is that in each case $G/P$ is the homogeneous model for a parabolic…