Related papers: Meromorphic almost rigid geometric structures

The study of quasi-K\"ahler Chern-flat almost Hermitian manifolds is strictly related to the study of anti-bi-invariant almost complex Lie algebras. In the present paper we show that quasi-K\"ahler Chern-flat almost Hermitian structures on…

We classify the 6-dimensional Lie algebras that can be endowed with an abelian complex structure and parameterize, on each of these algebras, the space of such structures up to holomorphic isomorphism.

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.…

We develop the theory of locally rigid and rigid symmetric monoidal $\infty$-categories over an arbitrary base $\mathcal{V}\in\mathrm{CAlg}(\mathbf{Pr}^\mathrm{L})$. Among other things, we prove that every locally rigid commutative…

Here, we classify Lie groups acting isometrically on compact Lorentz manifolds, and in particular we describe the geometric structure of compact homogeneous Lorentz manifolds.

In this paper we present some approaches to classification of almost complex structures and to construction of local or formal pseudoholomorphic mapping from one almost complex manifold to another. The corresponding criteria are given in…

We study locally compact group topologies on semisimple Lie groups. We show that the Lie group topology on such a group $S$ is very rigid: every 'abstract' isomorphism between $S$ and a locally compact and $\sigma$-compact group $\Gamma$ is…

Object of investigation are almost hypercomplex manifolds with Hermitian-Norden metrics of the lowest dimension. The considered manifolds are constructed on 4-dimensional Lie groups. It is established a relation between the classes of a…

On all compact complex surfaces (modulo finite unramified coverings), we classify all of the locally homogeneous geometric structures which are locally isomorphic to the exotic homogeneous surfaces of Lie.

We classify meromorphic affine connections on compact complex surfaces with algebraic dimension one, extending the work of Inoue,Kobayashi and Ochiai (1981) in the holomorphic case. The motivation is to investigate possible extension of the…

We study the six-dimensional solvmanifolds that admit complex structures of splitting type classifying the underlying solvable Lie algebras. In particular, many complex structures of this type exist on the Nakamura manifold $X$, and they…

A Lie group as a 4-dimensional pseudo-Riemannian manifold is considered. This manifold is equipped with an almost product structure and a Killing metric in two ways. In the first case Riemannian almost product manifold with nonintegrable…

We show how one can associate to a given class of finite type G-structures a classifying Lie algebroid. The corresponding Lie groupoid gives models for the different geometries that one can find in the class, and encodes also the different…

Our aim here is to investigate the holomorphic geometric structures on compact complex manifolds which may not be K\"ahler. We prove that holomorphic geometric structures of affine type on compact Calabi-Yau manifolds with polystable…

We present two constructions of complex symplectic structures on Lie algebras with large abelian ideals. In particular, we completely classify complex symplectic structures on almost abelian Lie algebras. By considering compact quotients of…

We study conformal Killing forms on compact 6-dimensional nearly K\"ahler manifolds. Our main result concerns forms of degree 3. Here we give a classification showing that all conformal Killing 3-forms are linear combinations of $d \omega$…

In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…

We study left-invariant generalized K\"ahler structures on almost abelian Lie groups, i.e., on solvable Lie groups with a codimension-one abelian normal subgroup. In particular, we classify six-dimensional almost abelian Lie groups which…

We introduce the notion of tight homomorphism into a locally compact group with nonvanishing bounded cohomology and study these homomorphisms in detail when the target is a Lie group of Hermitian type. Tight homomorphisms between Lie groups…

Using the algebraic classification of all $2$-dimensional algebras, we give the algebraic classification of all $2$-dimensional rigid, conservative and terminal algebras over an algebraically closed field of characteristic 0. We have the…