The Chern numbers of holomorphic vector bundles and formally holomorphic connections of complex vector bundles over almost complex manifolds.

1980 ◽  
Vol 1980 (314) ◽  
pp. 84-98
Keyword(s):  
Vector Bundles ◽  
Complex Manifolds ◽  
Complex Vector ◽  
Almost Complex Manifolds ◽  
Holomorphic Vector Bundles ◽  
Almost Complex ◽  
Chern Numbers

scholarly journals Lelong functional on almost complex manifolds

2014 ◽  
Vol 60 (2) ◽  
pp. 168-180
Author(s):  
Barbara Drinovec Drnovšek ◽  
Uroš Kuzman
Keyword(s):  
Complex Manifolds ◽  
Almost Complex Manifolds ◽  
Almost Complex

scholarly journals Holomorphic Vector Bundles on Holomorphically Convex Complex Manifolds

2006 ◽  
Vol 13 (1) ◽  
pp. 7-10
Author(s):  
Edoardo Ballico
Keyword(s):  
Vector Bundle ◽  
Complex Manifold ◽  
Vector Bundles ◽  
Open Neighborhood ◽  
Holomorphic Vector Bundle ◽  
Stein Manifold ◽  
Complex Manifolds ◽  
Holomorphic Vector Bundles

Abstract Let 𝑋 be a holomorphically convex complex manifold and Exc(𝑋) ⊆ 𝑋 the union of all positive dimensional compact analytic subsets of 𝑋. We assume that Exc(𝑋) ≠ 𝑋 and 𝑋 is not a Stein manifold. Here we prove the existence of a holomorphic vector bundle 𝐸 on 𝑋 such that is not holomorphically trivial for every open neighborhood 𝑈 of Exc(𝑋) and every integer 𝑚 ≥ 0. Furthermore, we study the existence of holomorphic vector bundles on such a neighborhood 𝑈, which are not extendable across a 2-concave point of ∂(𝑈).

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