Stability of Einstein-Hermitian vector bundles
type: Item
instance of: scholarly article
title: Stability of Einstein-Hermitian vector bundles
zbMATH Open document ID: 0558.53037
DOI: 10.1007/BF01169586
published in: Manuscripta Mathematica
publication date: 1983-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/154935
review text: On a compact Kähler manifold there is a close relationship between stable bundles in the sense of Mumford-Takemoto and the Einstein- Hermitian vector bundles of \textit{S. Kobayashi} [Einstein-Hermitian vector bundles and stability, Proc. Sympos. Global Riemannian Geometry, Durham, England 1982]. These Einstein-Hermitian bundles are Hermitian vector bundles with a certain restriction on their curvature. In this paper the author proves a theorem announced by Kobayashi: An Einstein-Hermitian bundle on a compact Kähler manifold is semi-stable and a direct sum of stable Einstein-Hermitian line bundles. The proof is short and efficient.
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 3890301
zbMATH Keywords: stable bundles
zbMATH Keywords: Einstein-Hermitian bundles
zbMATH Keywords: Kähler manifold
author: M. Lübke
reviewed by: M. Eastwood
MaRDI profile type: Publication
cites work: HOLOMORPHIC TENSORS AND VECTOR BUNDLES ON PROJECTIVE VARIETIES
cites work: The Extension Problem in Complex Analysis II; Embeddings with Positive Normal Bundle
cites work: Q4195061
cites work: Curvature and stability of vector bundles
cites work: First Chern class and holomorphic tensor fields
cites work: Q3685627
cites work: Vector bundles on complex projective spaces
OpenAlex ID: W2025523288
description: scientific article; zbMATH DE number 3890301