Related papers: Generalised Cartan Geometry
A new approach extending the concept of geometric phases to adiabatic open quantum systems described by density matrices (mixed states) is proposed. This new approach is based on an analogy between open quantum systems and dissipative…
This work extends previous developments carried out by some of the authors on Ehresmann connections on Atiyah Lie algebroids. In this paper, we study Cartan connections in a framework relying on two Atiyah Lie algebroids based on a…
Generalized geometry provides the framework for a systematic approach to non-symmetric metric gravity theory and naturally leads to an Einstein-Kalb-Ramond gravity theory with totally anti-symmetric contortion. The approach is related to…
On the generalized tangent bundle of a smooth manifold, we study skew-symmetric endomorphism satisfying an arbitrary polynomial equation with real constant coefficients. We study the compatibility of these structures with the de Rham…
The metric-affine and generalized geometries, respectively, are arguably the appropriate mathematical frameworks for Einstein's theory of gravity and the low-energy effective massless oriented closed bosonic string field theory. In fact,…
Elie Cartan's general equivalence problem is recast in the language of Lie algebroids. The resulting formalism, being coordinate and model-free, allows for a full geometric interpretation of Cartan's method of equivalence via reduction and…
We study generalized Kaehler manifolds for which the corresponding complex structures commute and classify completely the compact generalized Kaehler four-manifolds for which the induced complex structures yield opposite orientations.
We disclose the mathematical structure underlying the gauge field sector of the recently constructed non-abelian superconformal models in six spacetime dimensions. This is a coupled system of 1-form, 2-form, and 3-form gauge fields. We show…
Jets frames, that is a generalisation of ordinary frames on a manifold, are described in a language similar to that of gauge theory. This is achieved by constructing the Cartan geometry of a manifold with respect to the diffeomorphism…
We extend the universal differential calculus on an arbitrary Hopf algebra to a ``universal Cartan calculus''. This is accomplished by introducing inner derivations and Lie derivatives which act on the elements of the universal differential…
A rigid framework for the Cartan calculus of Lie derivatives, inner derivations, functions, and forms is proposed. The construction employs a semi-direct product of two graded Hopf algebras, the respective super-extensions of the deformed…
It is well--known that if one is given a principal $G$--bundle with a principal connection, then for every unitary finite--dimensional linear representation of $G$ one can induce a linear connection and a Hermitian structure on the…
We give a full classification of general affine connections on Galilei manifolds in terms of independently specifiable tensor fields. This generalises the well-known case of (torsional) Galilei connections, i.e. connections compatible with…
We reformulate the general theory of relativity in the language of Riemann-Cartan geometry. We start from the assumption that the space-time can be described as a non-Riemannian manifold, which, in addition to the metric field, is endowed…
The first part of the series formulates the Einstein-Cartan theory in the covariant hamiltonian framework. The first section revises the general multisymplectic approach and introduces the notion of the d-jet bundles. Since the whole…
Generalized parallelizable spaces allow a unified treatment of consistent maximally supersymmetric truncations of ten- and eleven-dimensional supergravity in generalized geometry. Known examples are spheres, twisted tori and hyperboloides.…
We present a generalised geometry framework for systematically constructing consistent truncations of ten- and eleven-dimensional supergravity preserving varying fractions of supersymmetry. Truncations arise when there is a reduced…
In the paper a Riemannian structure on the tangent bundle is defined by using a statistical structure $(g,\nabla)$ on the base manifold. Expressions for various curvatures of the structure are derived. Some rigidity results of the structure…
We pursue the study of holomorphic Cartan geometry with singularities. We introduce the notion of logarithmic Cartan geometry on a complex manifold, with polar part supported on a normal crossing divisor. In particular, we show that the…
This paper studies the infinitesimal structure of Carnot manifolds. By a Carnot manifold we mean a manifold together with a subbundle filtration of its tangent bundle which is compatible with the Lie bracket of vector fields. We introduce a…