Related papers: The canonical Cartan bundle and connection in CR g…
To certain types of generic distributions (subbundles in a tangent bundle) one can associate canonical Cartan connections. Many of these constructions fall into the class of parabolic geometries. The aim of this article is to show how…
The classical Cartan's structural equations show in a compact way the relation between a connection and its curvature, and reveals their geometric interpretation in terms of moving frames. In order to study the mathematical properties of…
We use the theory of Cartan connections to analyze the geometrical structures underpinning the gauge-theoretical descriptions of the gravitational interaction. According to the theory of Cartan connections, the spin connection $\omega$ and…
We explain what Cartan geometries are, aiming at an audience of graduate students familiar with manifolds, Lie groups and differential forms.
Tangent categories provide an axiomatic approach to key structural aspects of differential geometry that exist not only in the classical category of smooth manifolds but also in algebraic geometry, homological algebra, computer science, and…
A filtered manifold is a smooth manifold $M$ together with a filtration of the tangent bundle by smooth subbundles which is compatible with the Lie bracket of vector fields in a certain sense. The Lie bracket of vector fields then induces a…
Cartan's moving frames method is a standard tool in riemannian geometry. We set up the machinery for applying moving frames to cotangent bundles and its sub-bundles defined by non-holonomic constraints.
In this work we apply the Poincare-Cartan formalism of the Classical Field Theory to study the systems of balance equations (balance systems). We introduce the partial k-jet bundles of the configurational bundle and study their basic…
Let M be a simply connected Riemannian symmetric space, with at most one flat direction. We show that every Riemannian (or unitary) vector bundle with parallel curvature over M is an associated vector bundle of a canonical principal bundle,…
Cartan geometry provides a unifying algebraic construction of curvature and torsion, based on an underlying model Lie algebra -- a viewpoint that can be extended naturally to the higher algebraic structures underlying supergravity. We…
For a manifold $M$ endowed with a Legendrean (or Lagrangean) contact structure $E\oplus F \subset TM$, we give an elementary construction of an invariant partial connection on the quotient bundle $TM/F$. This permits us to develop a…
The construction of a linear connection on a pullback bundle from a connection on a vector bundle is explained in terms of fiberwise linear approximation. This procedure clarifies the geometric meaning of the linearized connection as well…
We give in this paper which is the fifth in a series of eight a theory of covariant derivatives of multivector and extensor fields based on the geometric calculus of an arbitrary smooth manifold M, and the notion of a connection extensor…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
We develop in detail the theory of c-projective geometry, a natural analogue of projective differential geometry adapted to complex manifolds. We realise it as a type of parabolic geometry and describe the associated Cartan or tractor…
A pedagogical but concise overview of fiber bundles and their connections is provided, in the context of gauge theories in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing…
In this paper we review the recently proposed path-integral counterpart of the Koopman-von Neumann operatorial approach to classical Hamiltonian mechanics. We identify in particular the geometrical variables entering this formulation and…
We present the general theory of curves in conformal geometry using tractor calculus. This primarily involves a tractorial determination of distinguished parametrizations and relative and absolute conformal invariants of generic curves. The…
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…
This paper describes the construction of a canonical compactification of the space of trajectories and of the unstable/stable sets of a generic gradient like vector field on a closed manifold as well as a canonical structure of a smooth…