Topic
Frame bundle
About: Frame bundle is a research topic. Over the lifetime, 1600 publications have been published within this topic receiving 23049 citations.
Papers published on a yearly basis
Papers
More filters
11 citations
01 Jul 1985
TL;DR: In this paper, the universal connection on the bundle of principal connections is used to stabilize the base manifold under perturbations of the chosen section, which reinforces the belief that general relativistic singularities cannot be removed by quantization.
Abstract: We make use of the universal connection on the bundle of principal connections; the bundle structure is governed by the action of the group on the first jet bundle. Each section determines a connection in the principal bundle, which in the case of the frame bundle allows a metric completion projecting onto the corresponding b- completion. It is shown that b -incompleteness of the base manifold is stable under perturbations of the chosen section. Hence, for instance, for (pseudo) Riemannian manifolds including spacetimes, b -incompleteness is a stable condition under conformal deformations of the metric. This reinforces the belief that general relativistic singularities cannot be removed by quantization.
11 citations
Journal Article•
TL;DR: In this article, the authors prove the existence of two natural families C(+) and C(-) of curves on the projective plane P(2), such that the Abel-Jacobi map F sends one of these families onto a copy of the theta divisor (Theta), and the other -- onto the jacobian J(X).
Abstract: Let the threefold X be a general smooth conic bundle over the projective plane P(2), and let (J(X), Theta) be the intermediate jacobian of X. In this paper we prove the existence of two natural families C(+) and C(-) of curves on X, such that the Abel-Jacobi map F sends one of these families onto a copy of the theta divisor (Theta), and the other -- onto the jacobian J(X). The general curve C of any of these two families is a section of the conic bundle projection, and our approach relates such C to a maximal subbundle of a rank 2 vector bundle E(C) on C, or -- to a minimal section of the ruled surface P(E(C)). The families C(+) and C(-) correspond to the two possible types of versal deformations of ruled surfaces over curves of fixed genus g(C). As an application, we find parameterizations of J(X) and (Theta) for certain classes of Fano threefolds, and study the sets Sing(Theta) of the singularities of (Theta).
11 citations
11 citations
01 Jan 2009
TL;DR: In this article, an intrinsic characterization is given of the concept of linear connection along the tangent bundle projection τ : TM → M, and the main observation is that every such connection D gives rise to a horizontal lift, which is needed to extend the action of the associated covariant derivative operator to tensor fields along τ in a meaningful way.
Abstract: An intrinsic characterization is given of the concept of linear connection along the tangent bundle projection τ : TM → M . The main observation thereby is that every such connection D gives rise to a horizontal lift, which is needed to extend the action of the associated covariant derivative operator to tensor fields along τ in a meaningful way. The interplay is discussed between the given D and various related connections, such as the canonical non-linear connection of the geodesic equations and certain linear connections on the pullback bundle τ∗τ . This is particularly relevant to understand similarities and differences between various notions of torsion and curvature. I further discuss aspects of variationality and metrizability of a linear D along τ and let me guide for the selected topics by a very short, old paper of Krupka and Sattarov.
10 citations