Related papers: Kaehler structures on Kc/(P,P)

The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.

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 survey different tools to classify representations of compact Lie groups according to their cohomogeneity and apply these methods to the case of irreducible representations of cohomogeneity 6, 7 and 8.

The first part of this paper surveys several characterizations of Teichm\"uller space as a subset of the space of representation of the fundamental group of a surface into PSL(2,R). Special emphasis is put on (bounded) cohomological…

We study the class $\mathcal{K}_{2}+\mathcal{K}_{4}$ of homogeneous pseudo-K\"ahler structures in the strongly degenerate case. The local form and the holonomy of a pseudo-K\"ahler manifold admitting such a structure is obtained, leading to…

To every $k$-dimensional modular invariant vector space we associate a modular form on $SL(2,\mathbb{Z})$ of weight $2k$. We explore number theoretic properties of this form and find a sufficient condition for its vanishing which yields…

A systematic study of the contributions at infinity for the cohomology of variations of polarized Hodge structures over quasicompact K\"ahler manifolds. Several isomorphisms between different cohomologies given.

We consider the commutative limit of matrix geometry described by a large-$N$ sequence of some Hermitian matrices. Under some assumptions, we show that the commutative geometry possesses a K\"{a}hler structure. We find an explicit relation…

The main purpose of the paper is to study hyperkahler structures from the viewpoint of symplectic geometry. We introduce a notion of hypersymplectic structures which encompasses that of hyperkahler structures. Motivated by the work of…

We prove an analogue of Kac's Theorem, describing the dimension vectors of indecomposable coherent sheaves, or parabolic bundles, over weighted projective lines. We use a theorem of Peng and Xiao to associate a Lie algebra to the category…

We introduce robust families of submanifolds for a linear Lie group $G$. We show that they give rise to geometric subspaces of the representation space ${\rm Hom}(\Gamma,G)$. As an application, we give a unified short proof of results of…

Lie groups of automorphisms of cotangent bundles of Lie groups are completely characterized and interesting results are obtained. We give prominence to the fact that the Lie groups of automorphisms of cotangent bundles of Lie groups are…

After a review of the general properties of holomorphic spheres in complex surfaces we describe the local geometry in the vicinity of a CP^1 embedded with a negative normal bundle. As a by-product, we build (asymptotically locally…

Let $P$ be a parabolic subgroup in $SL_n(\mathbb C)$. We show that there is a $SL_n(\mathbb C)$-stable closed subvariety of an affine Schubert variety in an infinite dimensional partial Flag variety (associated to the Kac-Moody group…

Let $G$ be a Lie group, and let $(g,J)$ be a left invariant almost pseudo-Hermitian structure on $G$. It is shown that if $(g,J)$ is also nearly pseudo-K\"{a}hler, then the tangent bundle $TG$ (with its natural Lie group structure induced…

We describe a geometric compactification of the moduli stack of left invariant complex structures on a fixed real Lie group or a fixed quotient. The extra points are CR structures transverse to a real foliation.

The geometry of symmetric spaces, polar actions, isoparametric submanifolds and spherical buildings is governed by spherical Weyl groups and simple Lie groups. A natural generalization of semisimple Lie groups are affine Kac-Moody groups as…

The Kaehler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kaehler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the…

In this paper we count the number of isomorphism classes of geometrically indecomposable quasi-parabolic structures of a given type on a given vector bundle on the projective line over a finite field. We give a conjectural cohomological…

We propose an deepened analysis of KV-Poisson structures of on IR^2. We present their classification their properties an their possible applications in different domains. We prove that these structure give rise to a new Cohomological…