Topic
Frame bundle
About: Frame bundle is a research topic. Over the lifetime, 1600 publications have been published within this topic receiving 23049 citations.
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TL;DR: In this paper, the concept of affine bundle of contact elements of type A on M was introduced and some affine properties of this bundle were described. But these properties were restricted to the case of Weil functors.
Abstract: . For every r-th order Weil functor T(A), we introduce
the underliyng k-th order Weil functors T(Ak), k=1,...,r-1. We
deduce that T(A)M -> T(Ar-1)M is an affine bundle for every
manifold M. Generalizing the classical concept of contakt
element by C. Ehresmann, we define the bundle of contact
elements of type A on M and we describe some affine properties
of this bundle.
19 citations
TL;DR: In this article, the main facts concerning the geometry of vector bundles on Calabi-Yau manifolds and constructions that enable them to embed them in the general context of modern physical concepts are presented.
Abstract: Vafa?[29] extended a?version of mirror symmetry to pairs consisting of a?Calabi-Yau manifold and a?fixed vector bundle on it. In?[30] he considered the mathematical meaning of this extension. In this paper we prove the main facts concerning the geometry of vector bundles on Calabi-Yau manifolds and describe all constructions that enable us to embed them in the general context of modern physical concepts.
19 citations
01 Jan 2003
TL;DR: Gauge Natural Field theories as mentioned in this paper generalize natural theories as well as pure gauge theories and to encompass many relevant physical situations, and they are considered for an arbitrary gauge natural theory.
Abstract: Gauge Natural field theories are introduced to generalize natural theories as well as pure gauge theories and to encompass many relevant physical situations. Conserved quantities and superpotentials are considered for an arbitrary gauge natural theory. Some relevant examples in Physics are considered in detail.
19 citations
01 Feb 1987
TL;DR: In this article, it was shown that any vector bundle E over a compact base manifold admits a complete metric of negative (respectively non-positive) curvature provided M admits a metric of positive (non-negative) curvatures.
Abstract: It is shown that any vector bundle E over a compact base manifold M admits a complete metric of negative (respectively nonpositive) curvature provided M admits a metric of negative (nonpositive) curvature.
19 citations
19 citations