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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0091-x,
author = {Jeffrey Case},
title = {Smooth metric measure spaces, quasi-Einstein metrics, and tractors},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {1733-1762},
zbl = {1263.53038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0091-x}
}
Jeffrey Case. Smooth metric measure spaces, quasi-Einstein metrics, and tractors. Open Mathematics, Tome 10 (2012) pp. 1733-1762. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0091-x/
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