The geometry of weakly selfdual Kahler surfaces

Details The geometry of weakly selfdual Kahler surfaces The geometry of weakly selfdual Kahler surfaces

2001-04-25

arxiv.org/abs/math/0104233v2

Compositio Math. 135 (2003) 279-322

Mathematics

Differential Geometry

LaTeX, 38 pages; two references added

Scientific paper

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.

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