A gauge theoretic approach to Einstein 4-manifolds

Joel Fine*, Kirill Krasnov, Dmitri Panov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

This article investigates a new gauge theoretic approach to Einstein's equations in dimension 4. Whilst aspects of the formalism are already explained in various places in the mathematics and physics literature, our first goal is to give a single coherent account of the theory in purely mathematical language. We then explain why the new approach may have important mathematical applications: the possibility of using the calculus of variations to find Einstein 4-manifolds, as well as links to symplectic topology. We also carry out some of the technical groundwork to attack these problems.

Original languageEnglish
Pages (from-to)293-323
Number of pages31
JournalNew york journal of mathematics
Volume20
Publication statusPublished - Apr 2014

Keywords

  • Einstein manifolds
  • 4-manifolds
  • gauge theory
  • QUATERNIONIC-KAHLER-MANIFOLDS
  • HYPERBOLIC GEOMETRY
  • RIGIDITY THEOREM
  • TWISTOR SPACES
  • CONSTANTS

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