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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 Burger-Roblin measure was shown to be ergodic for the frame bundle of a non-elementary convex cocompact hyperbolic 3 manifold with delta the critical exponent of its fundamental group.
Abstract: Let M be a non-elementary convex cocompact hyperbolic 3 manifold and delta the critical exponent of its fundamental group. We prove that a one-dimensional unipotent flow for the frame bundle of M is ergodic for the Burger-Roblin measure provided that delta>1.

3 citations

Posted Content
TL;DR: In this article, the problem of description of matter fields with an exact symmetry group with respect to a closed subgroup was addressed. But the problem was not addressed in this paper, since it is essential that matter fields admit an action of a gauge group.
Abstract: Higgs fields are attributes of classical gauge theory on a principal bundle $P\to X$ whose structure Lie group $G$ if is reducible to a closed subgroup $H$. They are represented by sections of the quotient bundle $P/H\to X$. A problem lies in description of matter fields with an exact symmetry group $H$. They are represented by sections of a composite bundle which is associated to an $H$-principal bundle $P\to P/H$. It is essential that they admit an action of a gauge group $G$.

3 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that the generalized (±) covariant differentiation is actually a special case of ordinary covariant divergence with respect to a connection on the principal fiber bundle having G 1(4,R)xG1(4,R) as its structure group.
Abstract: The bundle structures required by volume-preserving and related projective properties are developed and discussed in the context ofA(4) gauge theories which may be taken as the proper framework for Poincare gauge theories. The results of this paper include methods for extending both tensors and connections to a principal fiber bundle havingG1(4,R)xG1(4,R) as its structure group. This bundle structure is shown to be a natural arena for the generalized (±) covariant differentiation utilized by Einstein for his extended gravitational theories involving nonsymmetric connections. In particular, it is shown that this generalized (±) covariant differentiation is actually a special case of ordinary covariant differentiation with respect to a connection on theG1(4,R) xG1(4,R) bundle. These results are discussed in relation to certain properties of generalized gravitational theories based on a nonsymmetric connection which include the metric affine theories of Hehl et al. and the general requirement that it should be possible to formulate well-defined local conservation laws. In terms of the extended bundle structure considered in this paper, it is found that physically distinct particle number type conservation expressions could exist for certain given types of matter currents.

3 citations

Journal ArticleDOI
TL;DR: In this article, the authors consider a product preserving functor F of order r and a connection Γ on a manifold M and introduce horizontal lifts of tensor fields and linear connections from M to F(M) with respect to Γ.
Abstract: In this paper we consider a product preserving functor F of order r and a connection Γ of order r on a manifold M. We introduce horizontal lifts of tensor fields and linear connections from M to F(M) with respect to Γ. Our definitions and results generalize the particular cases of the tangent bundle and the tangent bundle of higher order.

3 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20236
202214
20214
202012
201911
201811