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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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23 citations
01 Nov 2002
TL;DR: In this paper, it was shown that there is a hypercomplex structure in the neighbourhood of the zero section of the tangent bundle TX of any complex manifold X with a real-analytic torsion-free connection compatible with the complex structure whose curvature is of type (1, 1).
Abstract: Using twistor techniques we shall show that there is a hypercomplex structure in the neighbourhood of the zero section of the tangent bundle TX of any complex manifold X with a real-analytic torsion-free connection compatible with the complex structure whose curvature is of type (1, 1). The zero section is totally geodesic and the Obata connection restricts to the given connection on the zero section.We also prove an analogous result for vector bundles: any vector bundle with real-analytic connection whose curvature is of type (1, 1) over X can be extended to a hyperholomorphic bundle over a neighbourhood of the zero section of TX.
22 citations
TL;DR: In this paper, the notion of frame bundles of the Brownian bridge is introduced and a Sobolev calculus is established over this frame bundle by using its functionals, and the associated stochastic gauge transform of this bundle over the original bridge is studied.
22 citations
01 Jan 1999
22 citations
Posted Content•
TL;DR: In this paper, the authors generalize Bolibruch's theorem from the projective line to curves of higher genus and show that an irreducible representation of the fundamental group of an open in a curve of high genus has always a representation as a regular system of differential equations on a semistable bundle of degree 0.
Abstract: This note is an attempt to generalize Bolibruch's theorem from the projective line to curves of higher genus. We show that an irreducible representation of the fundamental group of an open in a curve of higher genus has always a representation as a regular system of differential equations on a semistable bundle of degree 0. Vice-versa, we show that given such a bundle and 3 points on the curve, one can construct an irreducible representation of the curve minus the 3 points such that an associated regular system of differential equations lives on this bundle.
22 citations