Smooth metric measure spaces, quasi-Einstein metrics, and tractors
The author extends the tractor formalism from conformal geometry to the study of smooth metric measure spaces. In particular, this gives rise to a correspondence between quasi-Einstein metrics and parallel sections of certain tractor bundles. Using this formulation, he gives a sharp upper bound on the dimension of the vector space of quasi-Einstein metrics, providing a different perspective on some recent results of \textit{C. He} et al. [``On the classification of warped product Einstein metrics'' (submitted), Preprint \url{arXiv:1010.5488}; ``Uniqueness of warped product Einstein metrics and applications'' (submitted), Preprint, \url{arXiv:1110.2456}].
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