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Kähler-Einstein metrics of cohomogeneity one

✍ Scribed by Andrew Dancer; McKenzie Y. Wang

Publisher
Springer
Year
1998
Tongue
English
Weight
168 KB
Volume
312
Category
Article
ISSN
0025-5831

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Hyperkähler metrics of cohomogeneity one
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✍ Andrew Dancer; Andrew Swann 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 596 KB

Irreducible hyperk~ihler manifolds of dimension greater than four admitting a cohomogeneityone action of a compact simple Lie group are classified via coadjoint orbits. It is shown that the only complete example is the Calabi metric on T\*CP(n).

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We study a class of compact complex manifolds, with positive first Chern class, fibered over products of projective spaces. We prove that these bundles carry Einstein-Kähler metrics when the projective spaces of the basis have the same dimension. When this dimensional condition is not satisfied, we