Yang-Mills bar connections over compact Kähler manifolds

0342846 - MÚ 2011 RIV CZ eng J - Journal Article
Le, Hong-Van
Yang-Mills bar connections over compact Kähler manifolds.
Archivum mathematicum. Roč. 46, č. 1 (2010), s. 47-69. ISSN 0044-8753
R&D Projects: GA AV ČR IAA100190701
Institutional research plan: CEZ:AV0Z10190503
Keywords : Kähler manifold * complex vector bundle * holomorphic connection * Yang-Mills bar gradient flow
Subject RIV: BA - General Mathematics
http://www.dml.cz/handle/10338.dmlcz/139995

In this note we introduce a Yang-Mills bar equation on complex vector bundles E provided with a Hermitian metric over compact Hermitian manifolds. According to the Koszul-Malgrange criterion any holomorphic structure on E can be seen as a solution to this equation. We show the existence of a non-trivial solution to this equation over compact Kähler manifolds as well as a short time existence of a related negative Yang-Mills bar gradient flow. We also show a rigidity of holomorphic connections among a class of Yang-Mills bar connections over compact Käahler manifolds of positive Ricci curvature.
Permanent Link: http://hdl.handle.net/11104/0185466