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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 canonical singular hermitian metric with semipositive curvature current on the canonical line bundle of a compact Kahler manifold with pseudoeffective canonical bundle was constructed.
Abstract: We construct a canonical singular hermitian metric with semipositive curvature current on the canonical line bundle of a compact Kahler manifold with pseudoeffective canonical bundle
5 citations
TL;DR: In this article, a canonical family of Hermitian connections in a CR-holomorphic vector bundle (E,h) over a non-degenerate real hypersurface in a complex manifold was constructed, and an existence and uniqueness result for the solution to the inhomogeneous Yang-Mills equation was proved.
Abstract: We build a canonical family {Ds } of Hermitian connections in a Hermitian CR-holomorphic vector bundle (E,h ) over a nondegenerate CR manifold M, parametrized by S ∈ Γ ∞(End (E )), S skewsymmetric. Consequently, we prove an existence and uniqueness result for the solution to the inhomogeneous Yang-Mills equation dD*R D =f on M. As an application we solve for D ∈D (E,h ) when E is either the trivial line bundle, or a locally trivial CR-holomorphic vector bundle over a nondegenerate real hypersurface in a complex manifold, or a canonical bundle over a pseudo-Einstein CR manifold.
5 citations
Journal Article•
5 citations
TL;DR: In this article, it was shown that the tangent bundle of a smooth Banach manifold admits a vector bundle structure over the manifold if and only if the manifold is endowed with a linear connection.
Abstract: The tangent bundle $T^kM$ of order $k$, of a smooth Banach manifold $M$ consists of all equivalent classes of curves that agree up to their accelerations of order $k$. For a Banach manifold $M$ and a natural number $k$ first we determine a smooth manifold structure on $T^kM$ which also offers a fiber bundle structure for $(\pi_k,T^kM,M)$. Then we introduce a particular lift of linear connections on $M$ to geometrize $T^kM$ as a vector bundle over $M$. More precisely based on this lifted nonlinear connection we prove that $T^kM$ admits a vector bundle structure over $M$ if and only if $M$ is endowed with a linear connection. As a consequence applying this vector bundle structure we lift Riemannian metrics and Lagrangians from $M$ to $T^kM$. Also, using the projective limit techniques, we declare a generalized Fr\'echet vector bundle structure for $T^\infty M$ over $M$.
5 citations
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TL;DR: In this paper, the authors describe topological obstructions to embedding a complex matrix algebra bundle into a trivial one under some additional arithmetic condition on their dimensions, and explain a relation between this problem and some principal bundles with structure groupoid.
Abstract: In the present paper we describe topological obstructions to embedding of a (complex) matrix algebra bundle into a trivial one under some additional arithmetic condition on their dimensions. We explain a relation between this problem and some principal bundles with structure groupoid. Finally, we briefly discuss a relation of our results to the twisted K-theory.
5 citations