Tohoku Mathematical Journal

New examples of Sasaki-Einstein manifolds

Toshiki Mabuchi and Yasuhiro Nakagawa

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Abstract

In this note, stimulated by the existence result by Futaki, Ono and Wang for toric Sasaki-Einstein metrics, we obtain new examples of Sasaki-Einstein metrics on $S^1$-bundles associated to canonical line bundles of ${\boldsymbol P}^1({\boldsymbol C})$-bundles over Kähler-Einstein Fano manifolds, even though the Futaki's obstruction does not vanish. Here our examples include non-toric Sasaki-Einstein manifolds.

Article information

Source
Tohoku Math. J. (2), Volume 65, Number 2 (2013), 243-252.

Dates
First available in Project Euclid: 25 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1372182724

Digital Object Identifier
doi:10.2748/tmj/1372182724

Mathematical Reviews number (MathSciNet)
MR3079287

Zentralblatt MATH identifier
1288.53034

Subjects
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 32Q20: Kähler-Einstein manifolds [See also 53Cxx] 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]

Keywords
Sasaki manifolds Sasaki-Einstein metrics the Reeb field Kähler-Ricci solitons transverse holomorphic structures Koiso-Sakane's examples non-toric Sasaki-Einstein manifolds

Citation

Mabuchi, Toshiki; Nakagawa, Yasuhiro. New examples of Sasaki-Einstein manifolds. Tohoku Math. J. (2) 65 (2013), no. 2, 243--252. doi:10.2748/tmj/1372182724. https://projecteuclid.org/euclid.tmj/1372182724


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