Related papers: Subtleties Concerning Conformal Tractor Bundles
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…
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation…
This paper aims to classify the holonomy of the conformal Tractor connection, and relate these holonomies to the geometry of the underlying manifold. The conformally Einstein case is dealt with through the construction of metric cones,…
We obtain analogues of classical results on automorphism groups of holomorphic fiber bundles, in the setting of group schemes. Also, we establish a lifting property of the connected automorphism group, for torsors under abelian varieties.…
The theory of linear transports along paths in vector bundles, generalizing the parallel transports generated by linear connections, is developed. The normal frames for them are defined as ones in which their matrices are the identity…
Statistical manifolds, the parameter spaces of smooth families of probability density functions, are the central objects of study in information geometry. While the elementary differential geometry of Riemannian statistical manifolds is…
We show that infinitesimal automorphisms and infinitesimal deformations of parabolic geometries can be nicely described in terms of the twisted de-Rham sequence associated to a certain linear connection on the adjoint tractor bundle. For…
The general problem for consistency between arbitrary transports along paths in fibre bundles and bundle morphisms between them is formulated and investigated. The special case of one fibre bundle, its morphism and transport along paths…
In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…
The problem for consistency between linear transports along paths and real bundle metrics in real vector bundles is stated. Necessary and/or sufficient conditions, as well as conditions for existence, for such consistency are derived. All…
We introduce the concept of a graded bundle which is a natural generalization of the concept of a vector bundle and whose standard examples are higher tangent bundles T^nQ playing a fundamental role in higher order Lagrangian formalisms.…
We study the standard tractor bundle and the standard cotractor bundle of an almost Grassmann structure: We provide explicit formulae for their splitting operators, first BGG operators as well as prolongation connections. We characterize…
As a natural extension of the theory of uniform vector bundles on Fano manifolds, we consider uniform principal bundles, and study them by means of the associated flag bundles, as their natural projective geometric realizations. In this…
This article is devoted to investigations of a structure and homomorphisms of microbundles. Microbundles are generalizations of manifolds. For manifolds it was studied when their families of homomorphism can be supplied with the manifold…
These notes present elementary introduction to tractors based on classical examples, together with glimpses towards modern invariant differential calculus related to vast class of Cartan geometries, the so called parabolic geometries.
For a conformal manifold we introduce the notion of an ambient connection, an affine connection on an ambient manifold of the conformal manifold, possibly with torsion, and with conditions relating it to the conformal structure. The purpose…
Hermitian bundle gerbes with connection are geometric objects for which a notion of surface holonomy can be defined for closed oriented surfaces. We systematically introduce bundle gerbes by closing the pre-stack of trivial bundle gerbes…
It is known that all the vector bundles of the title can be obtained by holomorphic induction from representations of a certain parabolic Lie algebra on finite dimensional inner product spaces. The representations, and the induced bundles,…
For a compact, oriented, hyperbolic $n$-manifold $(M,g)$, realised as $M= \Gamma \backslash \mathbb{H}^{n}$ where $\Gamma$ is a torsion-free cocompact subgroup of $SO(n,1)$, we establish and study a relationship between differential…
Applying concepts and tools from classical tangent bundle geometry and using the apparatus of the calculus along the tangent bundle projection ('pull-back formalism'), first we enrich the known lists of the characterizations of affine…