Stability and Hermitian-Einstein metrics for vector bundles on framed manifolds

Stability and Hermitian-Einstein metrics for vector bundles on framed manifolds

The notions of stability of holomorphic vector bundles in the sense of Mumford-Takemoto and Hermitian-Einstein metrics in holomorphic vector bundles are adapted for canonically polarized framed manifolds, i. e. compact complex manifolds together with a smooth divisor admitting a certain projective e...

Full description

Saved in:
Bibliographic Details
Main Author: Stemmler, Matthias
Contributors: Schumacher, Georg (Prof. Dr.) (Thesis advisor)
Format: Doctoral Thesis
Language:English
Published: Philipps-Universität Marburg 2009
Subjects:
Mumford-Takemoto stability
Mumford-Takemoto-Stabilität
Gerahmte Mannigfaltigkeit
Kobayashi-Hitchin-Korrespondenz
Poincaré-Metrik
Mathematik
Kobayashi-Hitchin correspondence
Kähler-Mannigfaltigkeit
Kähler-Einstein-Metrik
Poincaré metric
Hermite-Einstein-Vektorraumbündel
Mathematics
Online Access:PDF Full Text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The notions of stability of holomorphic vector bundles in the sense of Mumford-Takemoto and Hermitian-Einstein metrics in holomorphic vector bundles are adapted for canonically polarized framed manifolds, i. e. compact complex manifolds together with a smooth divisor admitting a certain projective embedding. The main tool is the Poincaré metric, a special complete Kähler-Einstein metric on the complement of the divisor, whose asymptotic behaviour near the divisor is well-known due to results by Schumacher. The existence and uniqueness of Hermitian-Einstein connections in stable holomorphic vector bundles (Kobayashi-Hitchin correspondence) is proved in the setting of framed manifolds.
Physical Description:84 Pages
DOI:10.17192/z2010.0073

Similar Items