Related papers: Differential geometry of Cartan connections

We define what we call morphisms of Cartan connections. We generalize the main theorems on Cartan connections to theorems on morphisms. Many of the known constructions involving Cartan connections turn out to be examples of morphisms. We…

We give an explicit description, in terms of bracket, anchor, and pairing, of the standard cochain complex associated to a Courant algebroid. In this formulation, the differential satisfies a formula that is formally identical to the Cartan…

We calculate relations on characteristic classes which are obstructions preventing closed K\"ahler manifolds from carrying holomorphic Cartan geometries. We apply these relations to give global constraints on the phase spaces of complex…

We explain what Cartan geometries are, aiming at an audience of graduate students familiar with manifolds, Lie groups and differential forms.

A new notion of Cartan pairs as a substitute of notion of vector fields in noncommutative geometry is proposed. The correspondence between Cartan pairs and differential calculi is established.

We give a differential geometric description of the Cartan (or tractor) bundle and its canonical connection in CR geometry, thus offering a direct, alternative, definition to the usual abstract approach.

We extend the notion of connection in order to be able to study singular geometric structures, namely, we consider a notion of connection on a Lie algebroid which is a natural extension of the usual concept of connection. Using connections,…

This note shows the compatibility of the differential geometric and the topological formulations of equivariant characteristic classes for a compact connected Lie group action.

In this paper we study Cartan subalgebras in general and special linear algebras over a field of positive characteristic. We determined the conjugacy classes of Cartan subalgebras under the general linear groups, and count the explicit…

In this note we clarify the relevance of ``connections up to homotopy'' to the theory of characteristic classes. We have already remarked \cite{Crai} that such connections up to homotopy can be used to compute the classical Chern…

The characteristic forms in the bundle of connections of a principal bundle P over M determine the characteristic classes of P for degree less or equal to the dimension of M, and differential forms on the space of connections for higher…

We compute the characteristic Cartan connection associated with a system of third order ODEs. Our connection is different from Tanaka normal one, but still is uniquely associated with the system of third order ODEs. This allows us to find…

We classify compact manifolds of dimension three equipped with a path structure and a fixed contact form (which we refer to as a strict path structure) under the hypothesis that their automorphism group is non-compact. We use a Cartan…

With the intent of laying the groundwork for a program that aims at explicitly describing the space of Cartan (i.e. multiplicative) connections on a general proper Lie groupoid, we begin to investigate the space of such connections in the…

The chains studied in this paper generalize Chern-Moser chains for CR structures. They form a distinguished family of one dimensional submanifolds in manifolds endowed with a parabolic contact structure. Both the parabolic contact structure…

The aim of this note is to describe a geometric relation between simple plane curve singularities classified by simply laced Cartan matrices and cluster varieties of finite type also classified by the simply laced Cartan matrices. We…

We obtain relations among the characteristic classes of a manifold M admitting corank one maps. Our relations yield strong restrictions on the cobordism class of M and also nonexistence results for singular maps of the projective spaces. We…

Connections are an important tool of differential geometry. This paper investigates their definition and structure in the abstract setting of tangent categories. At this level of abstraction we derive several classically important results…

A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…

We give simple characterizations of contact 1-forms in terms of Dirac structures. We also relate normal almost contact structures to the theory of Dirac structures.