Related papers: Integrability of generalized structures on odd exa…

We introduce Hopf algebroid covariance on Woronowicz's differential calculus. Using it, we develop quite a general framework of noncommutative complex geometry that subsumes the one in [2]. We present transverse complex and K\"ahler…

We construct almost complex algebraic curvature tensors for pseudo Hermitian inner products whose skew-symmetric curvature operator has constant Jordan normal form on the set of non-degenerate complex lines.

We prove that a compact smooth 4-manifold admits generalized complex structures of odd type if and only if it has a transversely holomorphic 2-foliation. Consequently, there exist generalized complex structures of odd type on a circle…

We show that in analogy to the introduction of Poisson structures twisted by a closed 3-form by Park and Klimcik-Strobl, the study of three dimensional sigma models with Wess-Zumino term leads in a likewise way to twisting of Courant…

Two new classes of metrizable vector bundles have been presented in the papers [1] and [4]. The Lie algebroid generalized tangent bundle of a dual vector bundle is presented. This Lie algebroid is a new example of metrizable vector bundle.…

This article gives a survey of recent results on a generalization of the notion of a Hodge structure. The main example is related to the Fourier-Laplace transform of a variation of polarizable Hodge structure on the punctured affine line,…

A new class of completely integrable models is constructed. These models are deformations of the famous integrable and exactly solvable Gaudin models. In contrast with the latter, they are quasi-exactly solvable, i.e. admit the algebraic…

Let M be an almost complex manifold equipped with a Hermitian form such that its de Rham differential has Hodge type (3,0)+(0,3), for example a nearly Kahler manifold. We prove that any connected component of the moduli space of…

From a view point of the moment map, we shall introduce the notion of Einstein-Hermitian generalized connections over a generalized K\"ahler manifold of symplectic type. We show that moduli spaces of Einstein-Hermitian generalized…

We elaborate an unified geometric approach to classical mechanics, Riemann-Finsler spaces and gravity theories on Lie algebroids provided with nonlinear connection (N-connection) structure. There are investigated the conditions when the…

The subject of investigations are the almost hypercomplex manifolds with Hermitian and anti-Hermitian (Norden) metrics. A linear connection D is introduced such that the structure of these manifolds is parallel with respect to D and its…

A 2-plectic manifold is a manifold equipped with a closed nondegenerate 3-form, just as a symplectic manifold is equipped with a closed nondegenerate 2-form. In 2-plectic geometry we meet higher analogues of many structures familiar from…

We investigate a class of Leibniz algebroids which are invariant under diffeomorphisms and symmetries involving collections of closed forms. Under appropriate assumptions we arrive at a classification which in particular gives a…

Motivated by questions from quantum group and field theories, we review structures on manifolds that are weaker versions of Poisson structures, and variants of the notion of Lie algebroid. We give a simple definition of the Courant…

We consider normal almost contact structures on a Riemannian manifold and, through their associated sections of an ad-hoc twistor bundle, study their harmonicity, as sections or as maps. We rewrite these harmonicity equations in terms of…

We introduce the concept of Bergman bundle attached to a hermitian manifold X, assuming the manifold X to be compact - although the results are local for a large part. The Bergman bundle is some sort of infinite dimensional very ample…

A generalized notion of a Lie algebroid is presented. Using this, the Lie algebroid generalized tangent bundle is obtained. A new point of view over (linear) connections theory on a fiber bundle is presented. These connections are…

We describe how generalized complex geometry, which interpolates between complex and symplectic geometry, is compatible with T-duality, a relation between quantum field theories discovered by physicists. T-duality relates topologically…

We partially describe equivariant Dirac and generalized complex structures on a homogeneous space $G/K$ by giving equivalent data involving only the Lie algebra. We consider real semisimple adjoint orbits in any semisimple Lie algebra over…

We collect the recent results on invariant f-structures in the generalized Hermitian geometry. Here the canonical f-structures on homogeneous k-symmetric spaces play a remarkable role. Specifically, these structures provide a wealth of…