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.
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Case, J.S. Smooth metric measure spaces, quasi-Einstein metrics, and tractors. centr.eur.j.math. 10, 1733–1762 (2012). https://doi.org/10.2478/s11533-012-0091-x
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DOI: https://doi.org/10.2478/s11533-012-0091-x