Related papers: Flat Generalized Connections on Courant Algebroids

We prove that holomorphic normal projective connections on compact complex surfaces are flat. We show that a holomorphic torsion-free affine connection $\nabla$ on a compact complex surface is locally modelled on a translations-invariant…

In this paper, we study translation surfaces in the Euclidean space endowed with a canonical semi-symmetric non-metric connection. We completely classify the translation surfaces of constant sectional curvature with respect to this…

Let $X$ be an irreducible smooth complex projective variety. Let $G$ be a linear algebraic group over $\mathbb{C}$. We define the notion of Lie algebroid valued connection on holomorphic principal $G$--bundles on $X$, and study their basic…

We revisit the problem of integrating Lie algebroids $A\Rightarrow M$ to Lie groupoids $G\rightrightarrows M$, for the special case that the Lie algebroid $A$ is transitive. We obtain a geometric explanation of the Crainic-Fernandes…

The "metric" structure of nonrelativistic spacetimes consists of a one-form (the absolute clock) whose kernel is endowed with a positive-definite metric. Contrarily to the relativistic case, the metric structure and the torsion do not…

Classical contact Lie algebras are the fundamental algebraic structures on the manifolds of contact elements of configuration spaces in classical mechanics. In this paper, we determine the structure of the currently largest known category…

Symmetric connections that are compatible with semi-Riemannian metrics can be characterized using an existence result for an integral leaf of a (possibly non integrable) distribution. In this paper we give necessary and sufficient…

This paper studies linear generalised complex structures over vector bundles, as a generalised geometry version of holomorphic vector bundles. In an adapted linear splitting, a linear generalised complex structure on a vector bundle $E\to…

Courant algebroids provide a useful mathematical tool (not only) in string theory. It is thus important to define and examine their morphisms. To some extent, this was done before using an analogue of canonical relations known from…

Lie contact structures generalize the classical Lie sphere geometry of oriented hyperspheres in the standard sphere. They can be equivalently described as parabolic geometries corresponding to the contact grading of orthogonal real Lie…

We use the general setting for contrast (potential) functions in statistical and information geometry provided by Lie groupoids and Lie algebroids. The contrast functions are defined on Lie groupoids and give rise to two-forms and…

We study generic graded contractions of Lie algebras from the perspectives of group cohomology, affine algebraic geometry and monoidal categories. We show that generic graded contractions with a fixed support are classified by a certain…

We study the connectedness of the moduli space of gauge equivalence classes of flat G-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the…

We study integrability of generalized almost contact structures, and find conditions under which the main associated maximal isotropic vector bundles form Lie bialgebroids. These conditions differentiate the concept of generalized contact…

We study generalized Lie bialgebroids over a single point, that is, generalized Lie bialgebras. Lie bialgebras are examples of generalized Lie bialgebras. Moreover, we prove that the last ones can be considered as the infinitesimal…

We initiate a study of projections and modules over a noncommutative cylinder, a simple example of a noncompact noncommutative manifold. Since its algebraic structure turns out to have many similarities with the noncommutative torus, one…

D.Sullivan (1977) (see also the book by H.Whitney "Geometric Integration Theory",1957) considered a new model for underlying cochain complex for classical cohomologies with rational coefficients for arbitrary simplicial spaces that gives…

We study a few basic properties of Banach-Lie groupoids and algebroids, adapting some classical results on finite dimensional Lie groupoids. As an illustration of the general theory, we show that the notion of locally transitive Banach-Lie…

In this paper we study the local description of spaces of forms on transitive Lie algebroids. We use this local description to introduce global structures like metrics, $\ast$-Hodge operation and integration along the algebraic part of the…

Based on its central role in the framework of real calculi, the existence of the Levi-Civita connection for real calculi over projective modules is studied, with a special emphasis placed on the simple module of N-dimensional complex…