Related papers: Radially symmetric connections over round spheres

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

We give an alternative argument for the classification of real bundle pairs over smooth symmetric surfaces and extend this classification to nodal symmetric surfaces. We also classify the homotopy classes of automorphisms of real bundle…

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,…

We study flat vector bundles over complex parallelizable manifolds.

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…

This is a survey article on recent results on vector bundles on symmetric product of non-singular projective curves.

We investigate orthogonal and symplectic bundles with parabolic structure, over a curve.

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…

We quantize homogeneous vector bundles over an even complex sphere $\mathbb{S}^{2n}$ as one-sided projective modules over its quantized coordinate ring. We realize them in two different ways: as locally finite $\mathbb{C}$-homs between…

This paper gives various methods for constructing vector bundles over elliptic curves and more generally over families of elliptic curves. We construct universal families over generalized elliptic curves via spectral cover methods and also…

Any leafwise connection on a fibre bundle over a foliated manifold is proved to come from a connection on this fibre bundle.

This is a note in which we first review symmetries of moduli spaces of stable meromorphic connections on trivial vector bundles over the Riemann sphere, and next discuss symmetries of their integrable deformations as an application. In the…

We consider rationally connected complex projective manifolds M and show that their loop spaces--infinite dimensional complex manifolds--have properties similar to those of M. Furthermore, we give a finite dimensional application concerning…

A vector bundle with connection over a supermanifold leads naturally to a notion of parallel transport along superpaths. In this note we show that {\it every} such parallel transport along superpaths comes form a vector bundle with…

We prove that smooth 1-dimensional topological field theories over a manifold are equivalent to vector bundles with connection. The main novelty is our definition of the smooth 1-dimensional bordism category, which encodes cutting laws…

Working in univalent foundations, we investigate the symmetries of spheres, i.e., the types of the form $\mathbb{S}^n = \mathbb{S}^n$. The case of the circle has a slick answer: the symmetries of the circle form two copies of the circle.…

The aim of this paper is to write an explicit orthonormal parallelization for all parallelizable products of spheres, using an explicit isomorphism with a trivial vector bundle.

We give a method to construct stable vector bundles whose rank divides the degree over curves of genus bigger than one. The method complements the one given by Newstead. Finally, we make some systematic remarks and observations in…

Into this note we collect topics related to homogeneous vector bundles, elliptic adjoint orbits and so forth.

We consider when a smooth vector bundle endowed with a connection possesses non-trivial, local parallel sections. This is accomplished by means of a derived flag of subsets of the bundle. The procedure is algebraic and rests upon the…