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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, a vector bundle on a projective variety is isomorphic to a unique direct sum of indecomposable vector bundles (unique up to a permutation of the direct summands).
Abstract: We prove a principal bundle analog of a theorem on vector bundles that says that a vector bundle on a projective variety is isomorphic to a unique direct sum of indecomposable vector bundles (unique up to a permutation of the direct summands).
23 citations
Journal Article•
TL;DR: In this article, the tangent bundle of a wide class of Frechet manifolds is studied and a vector bundle structure is obtained with structural group a topological subgroup of the general linear group of the fiber type.
Abstract: The tangent bundle of a wide class of Frechet manifolds is studied he- re. A vector bundle structure is obtained with structural group a topological subgroup of the general linear group of the fiber type. Moreover, basic geo- metric results, known form the classical case of finite dimensional manifolds, are recovered here: Connections can be defined and are characterized by a generalized type of Christoffel symbols while, at the same time, parallel di- splacements of curves are possible despite the problems concerning differen- tial equations in Frechet spaces.
23 citations
TL;DR: In this paper, the existence of Dirac structures on the total space of a Poisson fiber bundle endowed with a compatible connection was studied and sufficient conditions for their existence were given.
Abstract: Poisson fiber bundles are studied. We give sufficient conditions for the existence of a Dirac structure on the total space of a Poisson fiber bundle endowed with a compatible connection. We also provide some examples.
23 citations
23 citations
TL;DR: In this paper, a bundle picture for singular symplectic quotients of cotangent bundles acted upon by lifted actions for the case that the configuration manifold is of single orbit type was developed.
Abstract: We develop a bundle picture for singular symplectic quotients of cotangent bundles acted upon by cotangent lifted actions for the case that the configuration manifold is of single orbit type. Furthermore, we give a formula for the reduced symplectic form in this setting. As an application of this bundle picture we consider Calogero–Moser systems with spin associated to polar representations of compact Lie groups.
23 citations