Smooth metric measure spaces, quasi-Einstein metrics, and tractors
Differential Geometry
2012-07-30 v3
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.
Keywords
Cite
@article{arxiv.1110.3009,
title = {Smooth metric measure spaces, quasi-Einstein metrics, and tractors},
author = {Jeffrey S. Case},
journal= {arXiv preprint arXiv:1110.3009},
year = {2012}
}
Comments
33 pages; final version