Abstract
In this paper we consider connections between Ricci solitons and Einstein metrics on homogeneous spaces. We show that a semi-algebraic Ricci soliton admits an Einstein one-dimensional extension if the soliton derivation can be chosen to be normal. Using our previous work on warped product Einstein metrics, we show that every normal semi-algebraic Ricci soliton also admits a k-dimensional Einstein extension for any k ≥ 2. We also prove converse theorems for these constructions and some geometric and topological structure results for homogeneous warped product Einstein metrics. In the appendix we give an alternative approach to semi-algebraic Ricci solitons which naturally leads to a definition of semi-algebraic Ricci solitons in the non-homogeneous setting.
Funding source: NSF
Award Identifier / Grant number: DMS 1006677
Funding source: NSF
Award Identifier / Grant number: DMS 0905527
Part of the work was done when the first author was at Lehigh University and he is very grateful to the institute for their hospitality.
© 2015 by De Gruyter
