Smooth metric measure spaces, quasi-Einstein metrics, and tractors

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Abstract

We introduce 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. We use this formulation to give a sharp upper bound on the dimension of the vector space of quasi-Einstein metrics, providing a different perspective on some recent results of He, Petersen and Wylie.

Original languageEnglish (US)
Pages (from-to)1733-1762
Number of pages30
JournalCentral European Journal of Mathematics
Volume10
Issue number5
DOIs
StatePublished - Oct 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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