Sharp metric obstructions for quasi-Einstein metrics

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Using the tractor calculus to study smooth metric measure spaces, we adapt results of Gover and Nurowski to give sharp metric obstructions to the existence of quasi-Einstein metrics on suitably generic manifolds. We do this by introducing an analogue of the Weyl tractor W to the setting of smooth metric measure spaces. The obstructions we obtain can be realized as tensorial invariants which are polynomial in the Riemann curvature tensor and its divergence. By taking suitable limits of their tensorial forms, we then find obstructions to the existence of static potentials, generalizing to higher dimensions a result of Bartnik and Tod, and to the existence of potentials for gradient Ricci solitons.

Original languageEnglish (US)
Pages (from-to)12-30
Number of pages19
JournalJournal of Geometry and Physics
Volume64
Issue number1
DOIs
StatePublished - Feb 1 2013

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Einstein Metrics
Obstruction
tractors
Metric Measure Space
Metric
Ricci Soliton
Curvature Tensor
calculus
Higher Dimensions
Divergence
divergence
Calculus
polynomials
solitary waves
curvature
tensors
analogs
Gradient
Analogue
gradients

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

Cite this

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Sharp metric obstructions for quasi-Einstein metrics. / Case, Jeffrey Steven.

In: Journal of Geometry and Physics, Vol. 64, No. 1, 01.02.2013, p. 12-30.

Research output: Contribution to journalArticle

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