The geometry of weakly selfdual Kahler surfaces

2001/04/30 by Vestislav Apostolov, David M. J. Calderbank, Paul Gauduchon
Mathematics · #math.DG #math.AG #msc:53C55 #msc:53C25 #msc:53B35

paper · pdf

published as Compositio Math. 135 (2003) 279-322 · LaTeX, 38 pages; two references added

arxiv created 2001/05/16 · arxiv updated 2009/11/30

Abstract

We study Kahler surfaces with harmonic anti-selfdual Weyl tensor. We provide an explicit local description, which we use to obtain the complete classification in the compact case. We give new examples of extremal Kahler metrics, including Kahler-Einstein metrics and conformally Einstein Kahler metrics. We also extend some of our results to almost Kahler 4-manifolds, providing new examples of Ricci-flat almost Kahler metrics which are not Kahler.

Related

• On weakly Einstein Kähler surfaces
• Almost-Kahler Anti-Self-Dual Metrics
• Four dimensional closed manifolds admit a weak harmonic Weyl metric
• Self-dual almost-Kähler four manifolds
• Classification of non-CSC extremal Kähler metrics on K-surfaces S²_\α\ and S²_\α,β\