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  1. 3 Open Mathematics

Autorzy help

  1. 2 Case J.

  2. 1 Graham C.

  3. 1 Willse T.

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  1. 1 2013

  2. 2 2012

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Subtleties concerning conformal tractor bundles

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Graham C., Willse T.
Open Mathematics
|
2012
|
tom 10
|
nr 5
1721-1732
EN
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.
2
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Smooth metric measure spaces, quasi-Einstein metrics, and tractors

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Case J.
Open Mathematics
|
2012
|
tom 10
|
nr 5
1733-1762
EN
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.
3
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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
EN
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.
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