Complete Ricci-flat Kähler manifolds of infinite topological type
✍ Scribed by Michael T. Anderson; Peter B. Kronheimer; Claude LeBrun
- Publisher
- Springer
- Year
- 1989
- Tongue
- English
- Weight
- 276 KB
- Volume
- 125
- Category
- Article
- ISSN
- 0010-3616
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## Abstract If a compact real hypersurface of contact‐type in a complex number space admits a Ricci soliton, then it is a sphere. A compact Hopf hypersurface in a non‐flat complex space form does not admit a Ricci soliton. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
An analogue of Calabi's conjecture was posed on a class of complete noncompact Kihler manifolds [5], then solved on the simplest of them, the complex n-space with n > 2 [9]. Here we prove the conjecture in its full generality, by inverting an elliptic complex Monge-Amp&e operator between suitable Fr