Invariant metrics on the tangent bundle of a homogeneous space

P. G. Walczak

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Displaying similar documents to “Invariant metrics on the tangent bundle of a homogeneous space”

Invariant metrics on the tangent bundle of a homogeneous space

P. G. Walczak (1978)

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Bollettino dell'Unione Matematica Italiana

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In this work we will analyze the relation between the stability and the simplicity of a homogeneous vector bundle on a projective variety. Our main theorem shows that a homogeneous bundle is not destabilized by its homogeneous subbundles if and only if it is the tensor product of a stable homogeneous bundle and an irreducible representation. Then we give an example of a homogeneous bundle, which is simple, but not stable.

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Let X be a differentiable manifold endowed with a transitive action α: A×X→X of a Lie group A. Let K be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects: equivalence classes of α-invariant K-connections on X α-invariant gauge classes of K-connections on X, andα-invariant isomorphism classes of pairs (Q,P) consisting of a holomorphic Kℂ-bundle Q → X and a K-reduction...

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The sudoku bundle provides a coordinated set of packages for displaying, solving, and generating Sudoku puzzles. This article describes some of the internal aspects of the packages.