Conformally warped manifolds, quasi-Einstein metrics, and tractors

Details Conformally warped manifolds, quasi-Einstein metrics, and tractors Conformally warped manifolds, quasi-Einstein metrics, and tractors

2011-10-13

arxiv.org/abs/1110.3009v1

Mathematics

Differential Geometry

38 pages

Scientific paper

We present a natural formulation of CWMs in the language of tractor bundles from conformal geometry. 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. We also use this formulation to mention some potentially interesting connections between conformal geometry, the study of quasi-Einstein metrics, and gradient Ricci solitons.

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