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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 derivative strings of Barndorff-Nielsen and the differential strings of Blaesild & Mora are considered from the coordinate-free viewpoint. And it is shown that the derivative string of given length and degree over a differentiable manifold form a vector bundle associated to a principal bundle of higher-order frames and that there is an analogous result for differential strings.
Abstract: The derivative strings of Barndorff-Nielsen and the differential strings of Blaesild & Mora are considered here from the coordinate-free viewpoint. It is shown that the derivative strings of given length and degree over a differentiable manifold form a vector bundle associated to a principal bundle of higher-order frames and that there is an analogous result for differential strings. Bundles of derivative strings are identified with vector bundles obtained from 0-truncated versions of Ehresmann's semi-holonomic jets by dualization and by taking tensor products. Similarly, bundles of differential strings are identified with vector bundles obtained from semiholonomic jets of certain tensor fields.
4 citations
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TL;DR: In this article, it was shown that a compact Kahler manifold with non-positive holomorphic sectional curvature has a canonical bundle and that the canonical bundle is ample, confirming a conjecture of Wu-Yau.
Abstract: We show that a compact Kahler manifold with nonpositive holomorphic sectional curvature has nef canonical bundle. If the holomorphic sectional curvature is negative then it follows that the canonical bundle is ample, confirming a conjecture of Yau. A key ingredient is the recent solution of this conjecture in the projective case by Wu-Yau.
4 citations
TL;DR: In this article, it was shown that the Jordan-Holder filtration admits a stable principal Higgs bundle on curves, and that the structure group of a semistable sheaves can be reduced to a parabolic subgroup of a reductive algebraic group over C such that the stable principal bundle is obtained by extending the structure groups to the Levi factor of the subgroup.
4 citations
4 citations
TL;DR: In this article, the authors examined the geometric properties of the horizontal distribution on a manifold in terms of the affine connection defined by T. Y. Thomas, and showed that the choice of a particular affine connect in the projective class corresponds to the selection of an horizontal distribution.
Abstract: The bundle of volume forms on a manifold is examined in terms of the affine connection defined by T. Y. Thomas. The choice of a particular affine connection in the projective class corresponds to the choice of an horizontal distribution on this bundle. The geometric properties of the horizontal distributions are studied. Special lifts of vector fields and covariant tensor fields are examined as well as lifts of metric connections.
4 citations