TY - JOUR
T1 - Smooth metric measure spaces, quasi-Einstein metrics, and tractors
AU - Case, Jeffrey S.
N1 - Funding Information:
The author is partially supported by NSF-DMS Grant No. 1004394.
PY - 2012/10
Y1 - 2012/10
N2 - 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.
AB - 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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U2 - 10.2478/s11533-012-0091-x
DO - 10.2478/s11533-012-0091-x
M3 - Article
AN - SCOPUS:84864428995
SN - 1895-1074
VL - 10
SP - 1733
EP - 1762
JO - Central European Journal of Mathematics
JF - Central European Journal of Mathematics
IS - 5
ER -