On Eta-Einstein Sasakian Geometry

Details On Eta-Einstein Sasakian Geometry On Eta-Einstein Sasakian Geometry

2004-06-30

arxiv.org/abs/math/0406627v4

Commun.Math.Phys.262:177-208,2006

Mathematics

Differential Geometry

31 pages, minor changes made, to appear in Commun. Math. Phys

Scientific paper

10.1007/s00220-005-1459-6

We study eta-Einstein geometry as a class of distinguished Riemannian metrics
on contact metric manifolds. In particular, we use a previous solution of the
Calabi problem for Sasakian geometry to prove the existence of eta-Einstein
structures on many different compact manifolds, including exotic spheres. We
also relate these results to the existence of Einstein-Weyl structures.

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