Related papers: On Connections and their Curvatures

In this note we consider a few interesting properties of discrete connections on principal bundles when the structure group of the bundle is an abelian Lie group. In particular, we show that the discrete connection form and its curvature…

We investigate relative holomorphic connections on a principal bundle over a family of compact complex manifolds. A sufficient condition is given for the existence of a relative holomorphic connection on a holomorphic principal bundle over…

This paper explores the relation between the structure of fibre bundles akin to those associated to a closed almost nonnegatively sectionally curved manifold and rational homotopy theory.

We present a collection of results on the evolution by curvature of networks of planar curves. We discuss in particular the existence of a solution and the analysis of singularities.

This work provides a curve-based approach to Ulrich bundles on surfaces, establishing a correspondence that characterizes their existence, with a focus on applications to surfaces in $\mathbb{P}^3$.

In the framework of Category Theory, we study the association between finite--dimensional representations of a compact quantum group and quantum vector bundles with linear connections for a given quantum principal bundle with a principal…

We give an account, in terms of fibered categories and their fibrewise duals, of aspects of the theory of bundle functors and star-bundle functors in differential geometry.

Following the approach of Budzy\'nski and Kondracki, we define covariant differential algebras and connections on locally trivial quantum principal fibre bundles. We also consider covariant derivatives, connection forms and curvatures and…

Consider a smooth proper holomorphic fibration of complex manifolds. It is known that the semipositivity of the curvature of the direct image of the relative canonical bundle can be read in terms of the cup product with the Kodaira-Spencer…

Partial connections are (singular) differential systems generalizing classical connections on principal bundles, yielding analogous decompositions for manifolds with nonfree group actions. Connection forms are interpreted as maps…

The purpose of this article is to present the theory of higher order connections on vector bundles from a viewpoint inspired by projective differential geometry.

In this review paper we discuss the different interpretations of the concept of connection in a fiber bundle and in a jet bundle, and relate it with first and second-order systems of partial differential equations (PDE's) and multivector…

A procedure is described to associate fibre bundles over the circle to two- dimensional theories with defects which have their field equations and defects described by a zero curvature condition.

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…

Transports along path in fibre bundles are axiomatically introduced. Their general functional form and some their simple properties are investigated. The relationships of the transports along paths and lifting of paths are studied.

We give a proof of the existence of radial (smooth) parallel sections of vector bundles endowed with a linear connection.

In this paper, we survey recent developments concerning the stability of naturally defined bundles on curves that play a central role in the deformation theory of the curve.

We present in the most natural way, that is, in the context of the theory of vector and principal bundles and connections in them, fundamental geometrical concepts related to General Relativity and one of its extensions, the Einstein-Cartan…

Let G be a Lie group. On the trivial principal G-bundle over the Lie algebra of G there is a natural connection whose curvature is the Lie bracket. The exponential map is given by parallel transport of this connection. If G is the…

A general formulation of zero curvature connections in a principle bundle is presented and some applications are discussed. It is proved that a related connection based on a prolongation in an associated bundle remains zero curvature as…