The geometry of weakly selfdual Kahler surfaces

David M.J. Calderbank; Paul Gauduchon; Vestislav Apostolov

The geometry of weakly selfdual Kahler surfaces

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arxiv math/0104233 v2 pith:PAD7CUHL submitted 2001-04-25 math.DG math.AG

Vestislav Apostolov , David M.J. Calderbank , Paul Gauduchon This is my paper · ORCID

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keywords kahlermetricsalmostexamplessurfacesanti-selfdualcaseclassification

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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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All toric Kahler surfaces with twistor 2-forms
hep-th 2024-12 conditional novelty 6.0 of 10

Smooth toric Kähler surfaces with a torus-invariant self-dual twistor 2-form fall into exactly six explicit local families: product-toric, Calabi-toric, orthotoric, elliptic, parabolic, and hyperbolic.

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