Holomorphic Bundles Trivializable by Proper Surjective Holomorphic Map

Surjective factorization of holomorphic mappings

We characterize the holomorphic mappings f between complex Banach spaces that may be written in the form f = T ◦ g, where g is another holomorphic mapping and T belongs to a closed surjective operator ideal.

Para-Kahler tangent bundles of constant para-holomorphic sectional curvature

We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagona...

Loop Groups and Holomorphic Bundles

This paper considers the links between the geometry of the various flag manifolds of loop groups and bundles over families of rational curves. Aa an application, a stability result for the moduli on a rational ruled surface of G-bundles with additional flag structure along a line is proven for any reductive group; this gives the corresponding stability statement for any compact group K for the ...

Higgs Bundles and Holomorphic Forms

For a complex manifold X which has a holomorphic form ̟ of odd degree k, we endow E = ⊕ p≥a Λ (p,0)(X) with a Higgs bundle structure θ given by θ(Z)(φ) := {i(Z)̟} ∧ φ. The properties such as curvature and stability of these and other Higgs bundles are examined. We prove (Theorem 2, section 2, for k > 1) E and additional classes of Higgs subbundles of E do not admit Higgs-Hermitian-Yang-Mills metr...

0 On Holomorphic Jet Bundles