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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, all first order Lagrangian densities on the bundle of connections associated to P that are invariant under the Lie algebra of infinitesimal automorphisms are shown to be variationally trivial and to give constant actions that equal the characteristic numbers of P if dimM is even and zero ifdimM is odd.
Abstract: Given a principal bundle P→M we classify all first order Lagrangian densities on the bundle of connections associated to P that are invariant under the Lie algebra of infinitesimal automorphisms. These are shown to be variationally trivial and to give constant actions that equal the characteristic numbers of P if dimM is even and zero if dimM is odd. In addition, we show that variationally trivial Lagrangians are characterized by the de Rham cohomology of the base manifold M and the characteristic classes of P of arbitrary degree

10 citations

Journal ArticleDOI
TL;DR: In this article, the authors present a formulation of the canonical transformations of Dirac theory by using the bundle of r−jets associated with the Dirac vector bundle, which allows them to study in a natural way (through an appropriate Noether theorem) the role which these canonical theories play in the definition of new symmetries.
Abstract: We present a formulation of the ’’canonical’’ transformations of the Dirac theory by using the bundle of r‐jets associated with the Dirac vector bundle. This allows us, by means of a variational principle previously introduced, to study in a natural way (through an appropriate Noether theorem) the role which these ’’canonical’’ theories play in the definition of ’’new’’ symmetries. The limit r→∞ corresponds to the equivalence between the canonical and the ordinary symmetries.

10 citations

Journal ArticleDOI
TL;DR: In this paper, a generalized notion of second order frame bundles is proposed, which is a principal Frechet bundle associated (differentially and geometrically) with the corresponding second order tangent bundle.

10 citations

Posted Content
TL;DR: In this paper, the authors construct canonical absolute parallelisms over real-analytic manifolds equipped with 2-nondegenerate hypersurface-type CR structures of arbitrary odd dimension not less than $7$ whose Levi kernel has constant rank.
Abstract: We construct canonical absolute parallelisms over real-analytic manifolds equipped with $2$-nondegenerate, hypersurface-type CR structures of arbitrary odd dimension not less than $7$ whose Levi kernel has constant rank belonging to a broad subclass of CR structures that we label as recoverable. For this we develop a new approach based on a reduction to a special flag structure, called the dynamical Legendrian contact structure, on the leaf space of the CR structure's associated Levi foliation. This extends the results of Porter-Zelenko [20] from the case of regular CR symbols constituting a discrete set in the set of all CR symbols to the case of the arbitrary CR symbols for which the original CR structure can be uniquely recovered from its corresponding dynamical Legendrian contact structure. Our method clarifies the relationship between the bigraded Tanaka prolongation of regular symbols developed in Porter-Zelenko [20] and their usual Tanaka prolongation, providing a geometric interpretation of conditions under which they are equal. Motivated by the search for homogeneous models with given nonregular symbol, we also describe a process of reduction from the original natural frame bundle, which is inevitable for structures with nonregular CR symbols. We demonstrate this reduction procedure for examples whose underlying manifolds have dimension $7$ and $9$. We show that, for any fixed rank $r>1$, in the set of all CR symbols associated with 2-nondegenerate, hypersurface-type CR manifolds of odd dimension greater than $4r+1$ with rank $r$ Levi kernel, the CR symbols not associated with any homogeneous model are generic, and, for $r=1$, the same result holds if the CR structure is pseudoconvex.

10 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the bundle connection of the Finsler-spacespace tangent bundle can be made compatible with Cartan's theory of FINSPACE by the inclusion of bundle torsion, without the restriction that the gauge curvature field be vanishing.
Abstract: It is demonstrated explicitly that the bundle connection of the Finslerspacetime tangent bundle can be made compatible with Cartan's theory of Finsler space by the inclusion of bundle torsion, and without the restriction that the gauge curvature field be vanishing. A component of the contorsion is made to cancel the contribution of the gauge curvature field to the relevant component of the bundle connection. Also, it is shown that the bundle manifold remains almost complex, and that the almost complex structure can be made to have a vanishing covariant derivative if additional conditions on the torsion are satisfied. However, the Finsler-spacetime tangent bundle remains complex only if the gauge curvature field vanishes.

10 citations

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