scholarly journals UNIFORMITY OF HOLOMORPHIC VECTOR BUNDLES ON INFINITE-DIMENSIONAL FLAG MANIFOLDS

2003 ◽  
Vol 40 (1) ◽  
pp. 85-89
Author(s):  
E. Ballico
Keyword(s):  
Vector Bundles ◽  
Flag Manifolds ◽  
Infinite Dimensional ◽  
Holomorphic Vector Bundles

HOMOGENEOUS VECTOR BUNDLES AND COWEN-DOUGLAS OPERATORS

1993 ◽  
Vol 04 (03) ◽  
pp. 503-520 ◽  
Author(s):  
DAVID R. WILKINS
Keyword(s):  
Vector Bundles ◽  
Symmetric Domain ◽  
Linear Operators ◽  
Open Unit ◽  
Bounded Symmetric Domain ◽  
Bounded Linear ◽  
Infinite Dimensional ◽  
Holomorphic Vector Bundles ◽  
Class B

In this paper we obtain an algebraic classification of all homogeneous Hermitian holomorphic vector bundles of arbitrary rank over a bounded symmetric domain. This classification result is used in order to classify, up to unitary equivalence, all irreducible homogeneous bounded linear operators on a separable infinite-dimensional Hilbert space that belong to the Cowen-Douglas class B2 (∆), where ∆ is the open unit disk.

Topologically trivial holomorphic vector bundles on infinite-dimensional projective varieties

2004 ◽  
Vol 134 (1) ◽  
pp. 33-38
Author(s):  
E. Ballico
Keyword(s):  
Vector Bundle ◽  
Finite Rank ◽  
Closed Subset ◽  
Vector Bundles ◽  
Complex Space ◽  
Holomorphic Vector Bundle ◽  
Projective Varieties ◽  
Infinite Dimensional ◽  
Holomorphic Vector Bundles ◽  
Locally Convex

Let V be an infinite-dimensional locally convex complex space, X a closed subset of P(V) defined by finitely many continuous homogeneous equations and E a holomorphic vector bundle on X with finite rank. Here we show that E is holomorphically trivial if it is topologically trivial and spanned by its global sections and in a few other cases.

Hermitian–Einstein metrics and jumping lines forSp(n+1)-homogeneous bundles over ℙ2n+1

1993 ◽  
Vol 114 (3) ◽  
pp. 443-451
Author(s):  
Al Vitter
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Vector Bundles ◽  
Einstein Metrics ◽  
Einstein Metric ◽  
Holomorphic Vector Bundles ◽  
Kähler Form ◽  
Points Of View ◽  
The Stability ◽  
Complex Projective

Stable holomorphic vector bundles over complex projective space ℙnhave been studied from both the differential-geometric and the algebraic-geometric points of view.On the differential-geometric side, the stability ofE-→ ℙncan be characterized by the existence of a unique hermitian–Einstein metric onE, i.e. a metric whose curvature matrix has trace-free part orthogonal to the Fubini–Study Kähler form of ℙn(see [6], [7], and [13]). Very little is known about this metric in general and the only explicit examples are the metrics on the tangent bundle of ℙnand the nullcorrelation bundle (see [9] and [10]).

Holomorphic Vector Bundles and the Geometry of ℙn

1980 ◽  
pp. 1-138
Author(s):  
Christian Okonek ◽  
Michael Schneider ◽  
Heinz Spindler
Keyword(s):  
Vector Bundles ◽  
Holomorphic Vector Bundles
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