New examples of Sasaki-Einstein manifolds
Toshiki Mabuchi, Yasuhiro Nakagawa
TL;DR
This paper presents new examples of Sasaki-Einstein manifolds, including non-toric cases, constructed on S^1-bundles over Kähler-Einstein Fano manifolds, expanding the known landscape of such geometries.
Contribution
It introduces novel Sasaki-Einstein metrics on S^1-bundles over Kähler-Einstein Fano manifolds, even when Futaki's obstruction is non-zero, using Sakane and Koiso's method.
Findings
New non-toric Sasaki-Einstein examples
Metrics on S^1-bundles over Fano manifolds
Examples with non-vanishing Futaki invariant
Abstract
In this note, stimulated by the existence result of Futaki-Ono-Wang for toric Sasaki-Einstein metrics, we obtain new examples of Sasaki-Einstein metrics on S^1-bundles associated to canonical line bundles of P^1-bundles over K\"ahler-Einstein Fano manifolds, even though the Futaki's obstruction does not vanish. Here the method of Sakane and Koiso is used, and our examples include non-toric Sasaki-Einstein manifolds.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory