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

Jeffrey Case

Open Mathematics (2012)

  • Volume: 10, Issue: 5, page 1733-1762
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Jeffrey Case. "Smooth metric measure spaces, quasi-Einstein metrics, and tractors." Open Mathematics 10.5 (2012): 1733-1762. <http://eudml.org/doc/269512>.

@article{JeffreyCase2012,
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.},
author = {Jeffrey Case},
journal = {Open Mathematics},
keywords = {Smooth metric measure space; Quasi-Einstein; Tractor bundle; Warped product; Holonomy; smooth metric measure space; quasi-Einstein; tractor bundle; holonomy},
language = {eng},
number = {5},
pages = {1733-1762},
title = {Smooth metric measure spaces, quasi-Einstein metrics, and tractors},
url = {http://eudml.org/doc/269512},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Jeffrey Case
TI - Smooth metric measure spaces, quasi-Einstein metrics, and tractors
JO - Open Mathematics
PY - 2012
VL - 10
IS - 5
SP - 1733
EP - 1762
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.
LA - eng
KW - Smooth metric measure space; Quasi-Einstein; Tractor bundle; Warped product; Holonomy; smooth metric measure space; quasi-Einstein; tractor bundle; holonomy
UR - http://eudml.org/doc/269512
ER -

References

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