Book Review: Differential geometry of complex vector bundles

Differential Geometry of Complex Vector Bundles

On the Differential Geometry of Homogeneous Vector Bundles

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Flat Complex Vector Bundles , the Beltrami Differential and W – Algebras

Since the appearance of the paper by Bilal et al. in '91, [1], it has been widely assumed that W –algebras originating from the Hamiltonian reduction of an SL(n, C)-bundle over a Riemann surface give rise to a flat connection, in which the Beltrami differential may be identified. In this letter, it is shown that the use of the Beltrami parametrisation of complex structures on a compact Riemann ...

Finsler Geometry of Projectivized Vector Bundles

Weak Equivalence Classes of Complex Vector Bundles

For any complex vector bundle Ek of rank k over a manifold Mm with Chern classes ci ∈ H2i(Mm, Z) and any non-negative integers l1, · · · , lk we show the existence of a positive number p(m, k) and the existence of a complex vector bundle Êk over Mm whose Chern classes are p(m, k) · li · ci ∈ H2i(Mm, Z). We also discuss a version of this statement for holomorphic vector bundles over projective a...