Akademik Veri Yönetim Sistemi
International Mathematics Research Notices, cilt.2013, sa.24, ss.5527-5570, 2013 (SCI-Expanded, Scopus)
We consider the stability of Sasaki-extremal metrics under deformations of the transversal complex structure of the foliation induced by the Reeb vector field ξ. Let g be a Sasaki-extremal metric on M, G a compact connected subgroup of the automorphism group of the Sasaki structure, and suppose the reduced scalar curvature satisfies. And consider a G-equivariant deformation of the transversely holomorphic foliation preserving as a smooth foliation. Provided the Futaki invariant relative to G of g is nondegenerate, the existence of Sasaki-extremal metrics is preserved under small variations of and of the Reeb vector in the center of. If G=T⊆Aut(g,ξ) is a maximal torus, the nondegeneracy of the Futaki invariant is automatic. So such deformations provide the easiest examples.When the initial metric g is Sasaki-Einstein and G=T⊆Aut(g,ξ) is a maximal torus a slice of the above family of Sasaki-extremal metrics is Sasaki-Einstein. Thus, for each there is a so that the Sasaki-extremal metric with Reeb vector field ξt is Sasaki-Einstein. We apply this to deformations of toric 3-Sasaki 7-manifolds to obtain new families of Sasaki-Einstein metrics on these manifolds, which are deformations of 3-Sasaki metrics. © 2012 The Author(s). Published by Oxford University Press. All rights reserved.