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Erratum to: “Smooth metric measure spaces, quasi-Einstein metrics, and tractors”

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Case J.

Open Mathematics

2013

tom 11

nr 1

196-196

The original version of the article was published in Central European Journal of Mathematics, 2012, 10(5), 1733–1762, DOI: 10.2478/s11533-012-0091-x. Unfortunately, it contains a typographical error in display of (27). Here we display the correct version of the equations.

Subtleties concerning conformal tractor bundles

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Graham C. , Willse T.

Open Mathematics

2012

tom 10

nr 5

1721-1732

The realization of tractor bundles as associated bundles in conformal geometry is studied. It is shown that different natural choices of principal bundle with normal Cartan connection corresponding to a given conformal manifold can give rise to topologically distinct associated tractor bundles for the same inducing representation. Consequences for homogeneous models and conformal holonomy are described. A careful presentation is made of background material concerning standard tractor bundles and equivalence between parabolic geometries and underlying structures.

Smooth metric measure spaces, quasi-Einstein metrics, and tractors

100%

Case J.

Open Mathematics

2012

tom 10

nr 5

1733-1762

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.