TY - JOUR
T1 - Uniqueness and examples of compact toric Sasaki-Einstein metrics
AU - Cho, Koji
AU - Futaki, Akito
AU - Ono, Hajime
PY - 2008/1
Y1 - 2008/1
N2 - In [11] it was proved that, given a compact toric Sasaki manifold with positive basic first Chern class and trivial first Chern class of the contact bundle, one can find a deformed Sasaki structure on which a Sasaki-Einstein metric exists. In the present paper we first prove the uniqueness of such Einstein metrics on compact toric Sasaki manifolds modulo the action of the identity component of the automorphism group for the transverse holomorphic structure, and secondly remark that the result of [11] implies the existence of compatible Einstein metrics on all compact Sasaki manifolds obtained from the toric diagrams with any height, or equivalently on all compact toric Sasaki manifolds whose cones have flat canonical bundle. We further show that there exists an infinite family of inequivalent toric Sasaki-Einstein metrics on S5 # k(S2 × S3) for each positive integer k.
AB - In [11] it was proved that, given a compact toric Sasaki manifold with positive basic first Chern class and trivial first Chern class of the contact bundle, one can find a deformed Sasaki structure on which a Sasaki-Einstein metric exists. In the present paper we first prove the uniqueness of such Einstein metrics on compact toric Sasaki manifolds modulo the action of the identity component of the automorphism group for the transverse holomorphic structure, and secondly remark that the result of [11] implies the existence of compatible Einstein metrics on all compact Sasaki manifolds obtained from the toric diagrams with any height, or equivalently on all compact toric Sasaki manifolds whose cones have flat canonical bundle. We further show that there exists an infinite family of inequivalent toric Sasaki-Einstein metrics on S5 # k(S2 × S3) for each positive integer k.
UR - http://www.scopus.com/inward/record.url?scp=36448984390&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=36448984390&partnerID=8YFLogxK
U2 - 10.1007/s00220-007-0374-4
DO - 10.1007/s00220-007-0374-4
M3 - Article
AN - SCOPUS:36448984390
VL - 277
SP - 439
EP - 458
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 2
ER -